Question

(1 point) Consider the series 4+(-4)" 8" Which of the following statements accurately describes the series? A. It converges to B. It converges to 38 C. It converges to 21 - D. It converges to E. None of the above, the series diverges.

Answer 1

Option (D) is correct.

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Ans given 도 껴 니 + -(-4)" 83 Y + (1) 꺄 87 83 + 9 8.8n- 껴 - + E 의 외 8 꺼 어 _ ) + () ()()) 의 1 - + - E ()() 거디

4 + (-4) n=1 N=l my Now the series! 20097+3 +4 +34) 2.1) (61*' and (0) ) are geometric series of the type of which are convergent for (r< 1 and divergent for 1rl7l, and if they are convergent then um will be s= I-r Now for 1) Cs)", comparing it with E, ara n=1 a e r= 1 8 bel=144 = Ś< so series Gh is convergent

and its sum will be S- a 은 - 느 (by 1 - 8 어 8 || 8. 용드복 ㅋ (3) () - 14 ㄱ n어 similarly comparing 9은께 M)

a 이 C Now Irl= 키리 드능시 뾿 싸 is convergent - So Me) and its sum will be :- Si 년 - ) ㅎ - ) [y) 긍 1+1 -18

2 2 s = M1 삐 3 putting 3 Dim ①: 9 ㄱ = 87 + (1) 옥 일 | 다. ㄱ 3 127

4+1-459 5 ㅋ - n=1 on so it converges to 5 is correct. 21 option 5 & D. It conve to converges