Chapter 10.2, Problem 42E

(d) Let an 6n²+ n-1 ntn and bn = √n n+1' (i) Determine whether {an} is convergent or divergent. Explain briefly. (ii) Determine whether Σ(-1)n-¹b, is convergent or divergent. Explain briefly. n=1

n as f • 27 (²) 2n n = 1 Evaluate | where f(x) => x" by identifying it as the value of a derivative or integral of geometric series. n = 0

l 12 and l13 solve both please

q11

. (a) Find the Taylor series of cos 2x at x = 0, either by direct calculation or by using the known series for cos x. (b) Use the trigonometric identity sin? x = }(1 – cos 2x) to find the Taylor series of sin² x at x = 0.

Find a power series, centered at 2, for the function f(x) = 1 and the interval 3x – 2 on which the expression is valid. OA. 5(-1)"3"(x – 2)" 4n+1 n=0 В. 3" (x – 2)" 4n+1 3 n=0

can you please help me answer the 2nd part of this question, the one about the interval? Thank you!

Pls solve this question correctly instantly in 5 min i will give u 3 like for sure

l14  and l15 solve both please