General term formula a(n+1)=(n+1)*a(n)+(-1)^(n+1) a(1)=0 It's better to write about the process

General term formula a(n+1)=(n+1)*a(n)+(-1)^(n+1) a(1)=0 It's better to write about the process

The original recursion is divided by (n + 1)! (! Denotes factorial) order
b(n) = a(n)/n!n=1,2,...
There are
b(n+1) = b(n) +(-1)^(n+1)/(n+1)!
b(1) = 0
therefore
b(1) = 0,
b(n) = 1/2!- 1/3!+ ...+ (-1)^n/ n!(n≥2)
Finally, we can reduce it to a (n)
a(1) = 0,
a(n) = n!*b(n) = n!* (1/2!- 1/3!+ ...+ (-1)^n/ n!) (n≥2)
How to do 4x + 14 = 28 + 3x
4x+14=28+3x
4x-3x+28-14
x=14
1. It is known that the triangle ABC is isosceles triangle o is the bottom edge BC, the midpoint circle O and waist AB are tangent to D, and it is proved that AC is tangent to circle o
2. Given the angle ABC = 60 degrees, the circle O with radius 1 cuts BC to C. if the circle O is rolled to the right on CB, what is the horizontal distance for the center O to move when the circle O is also tangent to Ca?
3. DB is the diameter of the semicircle, a is a point on the extension line of BD, AC cuts the semicircle to e, BC is perpendicular to C, and intersects the semicircle to F. given BD = 2, let ad = x, CF = y, then the analytic expressions of Y and X are?
1. The OE is perpendicular to AC,
Ao is the angular bisector, so OE = OD
The circle O is tangent to AB, so od = R (radius)
So OE = R
The distance from the center of the circle to AC is equal to the radius, so the circle is tangent to AC
Let CA cut ⊙ o 'at point E, CB cut ⊙ o' at point D, connect OO ', OC, o'd, o'e;
∵ AB is tangent to ⊙ o, ⊙ o ', AC is tangent to ⊙ o'
∴O'E⊥AC,O'D⊥BC,OC⊥BC
If the quadrilateral o'ocd is a rectangle, then OO '= CD
And ∵ ∠ ACB = 60 °
∴∠CO'D=1/2×∠EO'D=1/2×120°=60°
∴CD=√3×O'D
The radius of ⊙ O and ⊙ o 'is 1cm
∴OC=O'D=1cm
∴OO'=√3×1=√3(cm)
A: when rolling to the point where circle O and Ca are also tangent, the moving distance of circle center is √ 3cm/
3. Connect OE and DF to M
∵ AC cuts a circle O with diameter DB to E
∴OE⊥AC,DF⊥BC
∵AC⊥BC
The CEMF is a rectangle
OE//BC
∴EM=CF=y
BF=2OM=2(1-y)
Δ AOE is similar to Δ ABC
∴AO:AB=OE:BC
∴（1+x):(2+x)=1:(y+BF)
Y = x / (1 + x) = = I don't know if it's right
Formula of general term by superposition method
Given the n power of A1 = 3, an + 1 = an + 2 in the sequence, find the general term formula
An = a (n-1) + 2 ^ (n-1) a (n-1) = a (n-2) + 2 ^ (n-2) ---- A2 = a1 + 2. The above formulas add up to an + a (n-1) + - + A2 = a (n-1) + a (n-2) + - - + A2 + A1 + 1 + 2 + 4 + - - + 2 ^ (n-1) an = a1 + 2 + 4 + - - + 2 ^ (n-1) = 3 + 2 + 4 + 8 + - - + 2 ^ (n-1)
8.1 + 4x-3x = 10, you all know it!
How to calculate, give me the result in one minute, not just the result, quick
According to the principle of adding and subtracting the same number on both sides of the equation, the equation remains unchanged
8.1+4x-3x=10
4x-3x=10 -8.1
X=1.9
1. To make the value of function y = 6x + x ^ 2-2 greater than 0, the value range of X should be______________
2. The quadratic function y = x ^ 2 + 3x + 1, when x_____ Y > 0, X_____ Y < 0
3. A 100 meter long wire is used to form a rectangular chicken farm with one side against the wall. When the area of the rectangle is the largest, how many meters is its length longer than its width
The answers to the first two questions given upstairs are absolutely wrong!
If you can't type the root, just read it in order and write it on the paper
1. X ＞ radical 11-3 or X ＜ - (radical 11 + 3)
2. The first blank is: greater than (radical 5-3) / 2 or less than - (radical 5 + 3) / 2
The second null is greater than - (radical 5 + 3) / 2 and less than (radical 5-3) / 2
Suppose the length of rectangular chicken farm is x meters and the width is y meters
According to the meaning of the title, x + 2Y = 100, so x = 100-2y
When the area is the largest, that is, XY is the largest
Substituting x = 100-2y into XY, we get
-2Y ^ 2 + 100y: - (root 2 times y-50 / root 2) ^ 2 + 1250
When - (radical 2 times y-50 / radical 2) ^ 2 = 0, the maximum area is 1250
Solution - (root 2 times y-50 / root 2) ^ 2 = 0
y=25
Substituting x = 100-2y, we get x = 50
X-Y = 25m
So its length is 25 meters longer than its width
It's hard to type,
(1) X > 1 / 2 or X (- 3 + & 13), X
How to find the general term formula with the method of characteristic following
Can you give me an example
A (n + 2) - 3A (n + 1) + 2An = 0a1 = 1, A2 = 3, then the characteristic equation is x ^ 2-3x + 2 = 0x1 = 1, X2 = 2, so an = = C1 * X1 ^ n + C2 * x2 ^ n = C1 * 1 ^ n + C2 * 2 ^ n = C1 + C2 * 2 ^ n substitute A1 = 1, A2 = 3 into A1 = 1 = C1 + 2c2a2, A2 = 3 = C1 + 4c2c2 = 1, C1 = - 1An = - 1 + 2 ^ n
How to do 33 + 50 = x + (3x + 6) + 4x
33+50=83
x+(3x+6)+4x=x+4x+3x+6=(1+3+4)x+6=8x+6
So 83 = 8x + 6
So 8x = 83-6 = 77
So x = 77 / 8
3 answer to question 6
Let AC be x, so s = (10-x) divided by 2 gives the square of S = (X-5) + 25 divided by 2 and divides the whole by 1 / 2 of the negative
So when x = 5, there is a maximum, so when AC = 5, BD = 5 has the largest area
Using characteristic root method to find the general term formula of sequence
The eigenvalue method is only used to find the general term of the sequence which contains only an and an + 1 in the formula. That is to say, replace an and an + 1 with a letter X in the formula, and then it becomes an equation about X. solve the X case 1: if x has a solution, subtract the value of X from both sides of the original formula, and then both sides become reciprocal (the equation still holds)