n n→ ∞ b. n Give an example of a pair of series Σ a, and Σ b, with positive terms where lim n=1 n=1 (anb) = Σ a converges. Σb diverges, but = 0 and Σ bn n=1 n=1

Find the first four nonzero terms of the binomial series expansion of the function f (x) = (1 +x10)°. Simplify your answer. +.. + +

(10k - 12)- (7 – 4n) x > (-6m) 22.Evaluate the given series k=3 n=2 m=1 O A. -108 O B. -52 O C. 3574 O D. -3482

Q. Expand the following function in series form: (Questions are in the image attached.)

(-1) k 9. Does the series Ex=1 /27 Converge absolutely, converge conditionally or diverge? A. converges absolutely B. converges conditionally C. diverges B APY $ 5 t 11 ES OO

2. (a) Solve the difference equation Yt-3Yt-1 = 0 given Y₁ = 2. (b) Find the limit of the geometric series +/+/+...

-2b1) If E ak is convergent and (3ar- 2b) br is divergent, then Select one: a. Can't be determined (either converge or diverge) b. Converges c. Diverges The geometric series 3()* 1 converges to 2\k 3. k-1 Select one: 27 a. b. 9 C.4 Od. 13

Binomial seriesa. Find the first four nonzero terms of the binomial series centered at 0 for the given function.b. Use the first four terms of the series to approximate the given quantity.

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Q.4 - Determine whether the series converges, find its sum. converges or diverges. If it n=1