Summation of unequal difference and equal ratio sequence For example: find 1 / 2 + 3 / 4 + 7 / 8 +. + (the nth power of 2-1) / the nth power of 2?

Summation of unequal difference and equal ratio sequence For example: find 1 / 2 + 3 / 4 + 7 / 8 +. + (the nth power of 2-1) / the nth power of 2?

Original formula = 1-1 / 2 + 1-1 / 4 + 1-1 / 8 + 1-1 / 2 ^ n (n items in total)
=N - (1 / 2 + 1 / 4 + 1 / 8 + 1 / 2 ^ n)
＝n-[1-（1/2）^n]
＝n-1-1/2^n
The original formula = 1-1 / 2 + 1-1 / 4 + 1-1 / 8 +... + n power of 1-1 / 2
=N - (power n of 1 / 2 + 1 / 4 + 1 / 8 +... + 1 / 2)
=N - {(1 / 2) * [the nth power of 1 - (1 / 2)]} / (1-1 / 2)
=The nth power of N - (1 / 2) - 1
Summation of equal difference and equal ratio sequence
1 / 2 + 2 / 4 + 3 / 8 +. + n / (n power of 2)
Dislocation subtraction, no problem, it's just a little boring calculation, Sn = 1 * 1 / 2 + 2 * 1 / 2 ^ 2 + 3 * 1 / 2 ^ 3 + +n*1/2^n 1/2*Sn=1*1/2^2+2*1/2^3+………… +(n-1) * 1 / 2 ^ n + n * 1 / 2 ^ (n + 1) is subtracted to get 1 / 2 * Sn = 1 / 2 + 1 / 2 ^ 2 + 1 / 2 ^ 3 + +Before 1 / 2 ^ N-N * 1 / 2 ^ (n + 1)
What is the summation formula of arithmetic and ratio sequence?
Sum of arithmetic sequence: SN = n (a1 + an) / 2 or Sn = [2Na1 + n (n-1) D] / 2
Sum of equal ratio sequence: SN = A1 (1-Q ^ n) / (1-Q) or (A1 anq) / (1-Q)
There are some in mathematics books
Isochromatic s = (a1 + an) * n / 2
Equal ratio S = (a1-q * an) / (1-Q)
Three equilateral triangles with three sides of RT △ ABC are made outwards, and their areas are expressed by S1, S2 and S3 respectively, so as to determine the relationship among S1, S2 and S3
Area of equilateral triangle with side length a s = √ 3 * a * A / 4
Let the lengths of the three sides of RT triangle be a, B, C respectively, with a * a + b * b = C * C;
So S1 = √ 3A * A / 4; S2 = √ 3 * b * B / 4; S3 = √ 3 * c * C / 4;
So S1 + S2 = S3
OK? Ha ha, give me some points, Wuwu~
The sum of the areas of equilateral triangles with two right angled sides is equal to the area of equilateral triangles with hypotenuse: S1 + S2 = S3
The area formula is: S = 1 / 2 * a * a * sin60 (a is the edge)
So, S1: S2: S3 = a ^ 2: B ^ 2: C ^ 2
This is the relationship (a, B, c) with three sides
Mixed operation of addition and subtraction of mathematical rational numbers
1、{（-4）-（+7）}-（-5）
2、3-{（-3）-12}
3、8-（9-10）
4、（3-5)-(6-10）
5、13-{26-（21）+（-18）
6、{1.4-（-3.6+5.2）-4.3}-（-1.5）
7、|-2（1/4）-（-3/4）+1-|1-（1/2）|
Calculation: (1) - 5-9 + 3; (2) 10-17 + 8; (3) - 3-4 + 19-11; (4) - 8 + 12-16-23.2. Calculation: (1) - 4.2 + 5.7-8.4 + 10; (2) 6.1-3.7-4.9 + 1.8; (3) calculation: (1) (- 36) -(- 25) - (+ 36) + (+ 72); (2) (-)
（1）={（-4）-7}+5
=-11+5
=-6
（2）=3-（-15）
=3+15
=18
（3）=8-（-1）
=8+1
=9
（4）=（-2）-（-4）
=2
(5) One less bracket
（6）={1.4-4.6-4.3}+1.5
=-8.3+1.5
=6.8
(7) One less plus sign
What are the laws of subtraction and division
Subtraction: a-b-c = a - (B + C) Division: A / B / C = A / (b * c)
Subtraction has commutative law and associative law
Take the three sides of triangle as the diameter to make three semicircles. The area of the three semicircles from small to large is: s1s2s3. If S1 + S2 = S3, judge the shape of triangle ABC
ABC is a right triangle
Mixed operation of rational numbers
20, including the power, is a rational number calculation problem, don't know what a, B, X work out, the problem is a little difficult. See clearly and then answer, can plagiarize, but must meet the requirements
BC on the first floor, what's the answer
Do you want a set of papers with answers~
（1） Calculation questions:
(1)23+(-73) (2)(-84)+(-49) (3)7+(-2.04) (4)4.23+(-7.57) (5)(-7/3)+(-7/6) (6)9/4+(-3/2) (7)3.75+(2.25)+5/4 (8)-3.75+(+5/4)+(-1.5)
（2） It is calculated by a simple method
(1)(-17/4)+(-10/3)+(+13/3)+(11/3) (2)(-1.8)+(+0.2)+(-1.7)+(0.1)+(+1.8)+(+1.4)
（3） Known: x = + 17 (3 / 4), y = - 9 (5 / 11), z = - 2.25,
Find the value of (- x) + (- y) + Z
（4） With ">", "0", then A-ba (c) if BA (d) if AA, then B is_____________ (3) subtract - π from - 3.14, and the difference should be -____________ (4) if the subtracted is - 12 (4 / 5) and the difference is 4.2, then the subtracted should be -_____________ (5) if b-aa (c) 2A > AB (d) a / b > 1
（2） Fill in the blanks:
(1) When | a | / a = 1, a______________ When | a | / a = - 1, a______________ 0; (fill in >, 0, then a___________ If AB / C0, then B___________ (12) if a / b > 0, B / C (- 0.3) 4 > - 106 (b) (- 0.3) 4 > - 106 > (- 0.2) 3 (c) - 106 > (- 0.2) 3 > (- 0.3) 4 (d) (- 0.3) 4 > (- 0.2) 3 > - 106 (4) if a is a rational number and A2 > A, then the value range of a is () (a) A0 (d) A0 (c) a, B is opposite; (d) - AB (c) a
(5) The range of the exact number a indicated by the approximate number 1.20 obtained by the rounding method is ()
(A)1.195≤a
Mixed operation of addition and subtraction of rational numbers
The operation law of division
If the divisor remains unchanged and the divisor expands (or shrinks) several times, the quotient expands (or shrinks) the same multiple
If the divisor remains unchanged and the divisor is expanded (or reduced) several times, the quotient is reduced (or increased) by the same multiple
Take the three sides of RT triangle ABC as three semicircles, where S1, S2 and S3 represent the area of semicircles respectively, then the quantitative relationship of S1, S2 and S3 is
Pythagorean theorem, the area is the same. S1 + S2 = S3