Use the formula for the binomial series: (1 + x)" = = to obtain the Maclaurin series for (k + 7)! 1 + 8x + Σ k! k=2 1+ Σ (k + 8)! k! 8! 00 1 - 8x + 9! Σ(-1)+1 + 7! (+7 k! k=2 00 1 1 - 8x + Σ+1+7! 7! k! k=2 00 1 – 8x + k Σ (1) + 9! k! k=2 00 |- 1 (1 + x)8' με 1 + mx + έχ2 + ... + m(m-1) 2! m(m-1)...(m-k+1) k! 1+ Σκι m(m-1).(m-k+1) k! [x] < 1 exk if ark +

Q: If x= 5 213 + 5.7 31 3² + 5.7. 9 4:33 +..... ∞ ∞, then find the value of x²+4=

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Q: * (-1)" n=0 3n + 1 8.5.10. Find the sum

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Q: Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k!…

A: 1 + xm = 1+ mx + ∑k - 2∞m(m - 1)(m - 2) ... (m - k + 1)k!xk if x &lt;1 is the binomial expansion. We…

Q: Use power series to show that 1 1 1 e =- + 0! +...** 2! 3! 4! 5! 6! 117

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Q: 1+x Find the Maclaurin series for the In, 1-x

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Q: Find the Maclaurin series for the given function. SELECT A) B) sin(10z) (-1)*102m+1,an (2n + 1)! 8…

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Q: By applying the ratio test to the series (2n)" n!- (6e)" 7. we conclude that: o the series is…

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Q: Find the limit of the series 3-1 + 3-2 + 3-3 + ...+ 3-n+ ... additionally, write the sum in sigma…

A: Given: series is 3-1+3-2+3-3+…+3-n+… To be find: limit of the series and write sum in sigma…

Q: Use the formula for the binomial series: (1 + x)" 1+ mx + m(m-1)2 + m(m–1)--(m–-k+1), + + ... k!…

A: We need to find Maclaurin series for , 11 + x3. We have given that ,  1 + xm = 1 + mx + m(m-1)2!x2 +…

Q: Find the sum of the series. n = 0 7(-1)^2n + 1 22n + 1(2n + 1)! X

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Q: 32 – 20 33 - 21 51 52 3k+1_ 2*-1 + ... +...

A: Given: S=32-2051+33-2152+...........+3k+1-2k-15k+......... for evaluating given summation first we…

Q: verify that the series diverges

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the sum of the series S. 3- 3 In(8) 3 (In(8))? - 3 (In(8))³ _ ... 2! 3!

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: +∞ Σ η=1 η n' + 1

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Q: Find the Maclaurin series for the given function. A) B) 6+z (-1)"z*+1 6 (-1)"z" o 6+1 D) (-1)"z"…

A: In this question we have to find the Maclaurin series of the function.

Q: x7 – 6x8 + 62x9 2! 63 x 10 3! + 64x11 4!

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Q: 15 sum of the series 3n-1X3nt 2)

A: We have to find sum

Q: 29. Which of the following is a power series expansion of 6 X 2n X x (A) 1 + + + + + 2! 6! (2n)! 6 X…

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Q: 1. Describe the convergence of the series 3! + 3² + + (n+1)² (n + 2)! +

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Q: In this question you should assume that –1<x<1. (a) For the binomial expansion of (1-x) (1) find and…

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Q: (a) Give an instance of the Binomial Series which begins as follows: 10 1 - 6z² +24z¹ - 80z6 +240z8…

A: Given binomial series Note: According to the guidelines we are allowed to solve one question at a…

Q: Since the MacLaurin series for In(3 + x) is In A+ -1)"+1 nB -", which of the following are n=1 A and…

A: We have to use standard Taylor series of a standard function.