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Summation formula of equal ratio sequence
A (n + 1) / an = q, n is a natural number
(2) The general formula is: an = A1 * q ^ (n-1);
The generalized formula is: an = am · Q ^ (n-m);
(3) Sum formula: SN = n * A1 (q = 1)
Sn=a1(1-q^n)/(1-q)
=(a1-a1q^n)/(1-q)
=A1 / (1-Q) - A1 / (1-Q) * q ^ n (i.e. a-aq ^ n)
(premise: q is not equal to 1)
What does each letter of the summation formula of the equal ratio sequence represent
What do the letters A1 (1-qn) / 1-Q stand for
And I'm going to put this formula in
1+2+2²2+2²3+2²4+2²5.+2²2008
If the answer is clear, 50 points is yours
1 + 2 + 2's square + 2's third power + 2's fourth power + 2's fifth power +. 2's 2008 power =?
If your last term is the square of 2 multiplied by 2008, then 2 & sup2; 2 + 2 & sup2; 3 + 2 & sup2; 4 + 2 & sup2; 5. + 2 & sup2; 2008 is the arithmetic sequence. Arithmetic: SN = n (a1 + an) / 2 1 + 2 + 2 & sup2; 2 + 2 & sup2; 3 + 2 & sup2; 4 + 2 & sup2; 5. + 2 & sup2; 2008 = 3 + 2 & sup2; 2 + 2 & su
Some common formulas of arithmetic sequence and ratio sequence
General term formula of arithmetic sequence
an=a1+（n-1)d
Sum formula of the first n terms of arithmetic sequence
Sn=n×a1+n(n-1)d/2
or
Sn=n(a1+an)/2
Other formula theorems of arithmetic sequence
①a(n-k)+a(n+k)=2an
(as A3 + A5 = 2a4 or A5 + A10 = 2a7, and K can be any positive integer less than n)
② If M + n = P + Q
Then am + an = AP + aq
③(am-an)/(m-n)=d
④ If {an} and {BN} are both arithmetic sequences, then {a (BN)} and {B (an)} are also arithmetic sequences
Determination method of arithmetic sequence
① A (n + 1) - an = constant
②a(n-1)+a(n+1)=2an
The first n terms of arithmetic sequence and other formulas
S（9n)-S（8n)=S（8n)-S（7n)=S（7n)-S（6n)=...=n^2d
General term formula of equal ratio sequence
an=a1×q^(n-1)
The sum formula of the first n terms of the equal ratio sequence
An = A1 [1-Q ^ (n-1)] / (1-Q) (when Q ≠ 1)
An = n × A1 (when q = 1)
Other formula theorems of equal ratio sequence
①a(n-k)×a(n+k)=an^2
② If M × n = P × Q
Then am × an = AP × aq
③ (m-n) √ (am an) = q (note that M-N here refers to the power of m-n)
A method to determine whether it is an equal ratio sequence
① A (n + 1) / an = constant
②a(n-1)×a(n+1)=an^2
Give yourself a question about the mixed operation of positive and negative numbers ~ addition and subtraction in Volume 1 of Grade 7 (the more difficult the better), the process (the more words in the process, the better),
1+2-3-4+5+6-7-8+.+2005+2006-2007-2
What is the value of 008?
The result of each group was - 4, a total of 2008 / 4 = 502 groups
502*-4+-2008
3+2-77+195=123
It's a problem
Division is the inverse of multiplication. Multiplication is the inverse of division, right
Division is the inverse of multiplication. Is multiplication the inverse of division?
Yes, they are inverses of each other
If any two elements of a and B in the set are given the operation rule, we can determine that a and B are the only elements of a and C in the set, One of B can get another element according to a certain rule. This rule also defines an operation, which is called the inverse operation of the original operation, such as addition and subtraction, multiplication and division, power and logarithm
In the circuit as shown in the figure, the power supply voltage remains unchanged, and the switch S is in the closed state. When the switches S1 and S3 are open and S2 is closed, the total electric power of resistance R1 and R2 is P1, and P1 = 6.4w, and the voltage is U1; when S1 is open and S2 and S3 are closed, the power of resistance R2 is P2, and P2 = 6W, and the voltage is U2; when S1 is closed and S2 and S3 are closed, the current is 1.6A : U2 = 4:3. Find (1) supply voltage. (2) resistance R3
It is known that: P1 = 6.4w, P2 = 6W, I = 1.6A, U1: U2 = 4:3 find: u, R3 when switches S1 and S3 are open and S2 is closed, three resistors are connected in series, namely: P1 = U1 × & nbsp; u − u1r3 (1) or P1 = u21r1 + R2 (4) when switches S1 and S3 are open and S2 and S3 are closed, resistance R2 is connected in series with R3, and voltmeter measures voltage at both ends of R2, namely: P2 = & nbsp; U2 × u − u2r3 (2) when S1 is closed and S2 and S3 is disconnected, resistance R1 and R2 are connected in series, and the current representation can be expressed as: 1.6A = ur1 + R2 (3) divide (1) and (2) to get: p1p2 = U1 (U − U1) U2 (U − U2) 6.4w6w = 4 (U − U1) 3 (U − U2) u = 2u1 divide (3) and (4) to get: p11.6a = u21uu = 14u12, so 2u1 = 14u21, then U1 = 8V, so the power supply voltage is: u = 2 × 8V = 16V; divide (3) and (4) to get: p11.6a = u21u = 14u21, so 2u21 = 14u21, then U1 = 8V Substituting the source voltage and U1 into (1) formula, R3 = 8V (16V − 8V) 6.4w = 10 Ω answer: the power supply voltage is 16V, and the resistance of R3 is 10 Ω
Five difficult mathematical problems in volume one of grade seven
The derivation process of the volume formula of the ball
What I learned in high school is wrong upstairs``````
The center of a cylinder with the bottom radius R and height R is cut out of a circular cone with the same bottom and height. The area of the remaining part is equal to that of a hemisphere when it is cut by a plane. We can draw the conclusion that their volume is equal. The volume of the excavated body is easy to find. It is the volume of the hemisphere. V = 2 / 3 π R ^ 3. Therefore, the volume of a whole sphere is 4 / 3 π R ^ 3. The sphere is formed by circular rotation. The area of the circle is s = π R ^ 2, Then the sphere is its integral and the volume formula of the sphere is v = 4 / 3 π R ^ 3
You can learn from Edison, dig a small eye of the ball, fill it with water, and then pour the water into the measuring cup to calculate the volume!
In the circuit as shown in the figure, the power supply voltage remains unchanged, and the switch S is in the closed state. When the switches S1 and S3 are open and S2 is closed, the total electric power of resistance R1 and R2 is P1, and P1 = 6.4w, and the voltage is U1; when S1 is open and S2 and S3 are closed, the power of resistance R2 is P2, and P2 = 6W, and the voltage is U2; when S1 is closed and S2 and S3 are closed, the current is 1.6A : U2 = 4:3. Find (1) supply voltage. (2) resistance R3
It is known that: P1 = 6.4w, P2 = 6W, I = 1.6A, U1: U2 = 4:3 find: u, R3 when switches S1 and S3 are open and S2 is closed, three resistors are in series, that is: P1 = U1 × & nbsp; u − u1r3 (1) or P1 = u21r1 + R2 (4) when switches S1 and S3 are open and S2 and S3 are closed, resistance R2 is in series with R3, and voltmeter measures the voltage at both ends of R2
There is a question "when a = 2, B = - 2, find the value of the polynomial 3A ^ 3B ^ 3-0.5a ^ 2B + B - (4a ^ 3B ^ 3-0.25a ^ 2b) + (a ^ 3B ^ 3 + 0.25A ^ 2b) - 2b ^ 2 + 3". Ma Xiaohu wrongly copied a = 2 into a = - 2, Wang Xiaozhen did not copy the wrong question, but they all made the same results. Do you know what happened? Explain the reason
^It's Square
Because it's a coincidence that there are no brackets in front of the number, ha ha, it's very accurate - I hope it can help you ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~·
If we simplify the polynomial first, maybe a doesn't exist, so the value of the whole polynomial has nothing to do with a
I didn't count it because I really don't know what ^ means... Square?
Although you have explained ^, this formula is still a little difficult for me
I can't understand the polynomial in front of 3A ^ 3B ^ 3-0.5a ^ 2B + B. let's read LZ
3A * 3B * 3? ... unfold
If we simplify the polynomial first, maybe a doesn't exist, so the value of the whole polynomial has nothing to do with a
I didn't count it because I really don't know what ^ means... Square?
Although you have explained ^, this formula is still a little difficult for me
I can't understand the polynomial in front of 3A ^ 3B ^ 3-0.5a ^ 2B + B. let's read LZ
3A * 3B * 3? Put it away
A, positive or negative, is squared off. Square is a positive number. 2 squared is 4. - 2 squared is 4
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