Question

Determine whether the following series converges or diverges. 2k E VK²+7 k= 0 V Choose the correct answer below. O A. According to the Divergence Test, the series diverges because lim ak +0. k→ B. According to the Divergence Test, the series converges because lim ak = 0. k+00 OC. According to the Divergence Test, the series diverges because lim ak = 0. ko D. According to the Divergence Test, the series converges because lim ak +0. ko O E. The Divergence Test is inconclusive.

Answer 1

Option (A) is correct.

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QK Any E k=Ok² +7 E ak k=o Here ak= QK JKT Divergence Test: Consider the sesies E ak. If k=o lim auto k-) then geven series is divergent.

Now as k too, so Now lim ax = lim K- Qk (by @) K- ✓k +7 ok lim koo Jk² (1+1 2 2 - lim 2k kos (as J K = iki lkl It 7 2 k (No ko = 1 kl=k as 1x1=x it xzo and 1x1= -x if xlo

lim ak Kyo Klit +7 ka lo = lim kyoo It? ko

= Ja + 7 فرصة) 오 aso9a ītis īt if noo 쁠 VI+o . 9

1 우 So lim ar=2 to ko - lim ax to kto So answer is According to the Divergence Test, the series diverges because lim auto ktoo (option A is correct)