Question

Ex. 2.12. Miscellaneous. Determine whether the following series are con- vergent or divergent. Zn2 En m3 m3"(7) n2 +n (1+n2 n=1 n = © SUT, May 23, 2019 64 Module 2. Numerical Series N= 0 Vn2 +1-n (3n)! nn!)3 n2 + Inn vn n=1 ( 8 (-:-)" so Živa – vn = 1)

only answer number 4

Answer 1

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(iv) -> No, Tn Now, let's cosider E Then and Inx both increasimg The uhen xe[2, 0) So fx) is decreas ing and Lim fcx) = 0 Hence, by Cauchy condensation test, z n) and X M22 n=2 diverges together (Heve aen-13) converges o r Jet a=2. Then 乏 2'f(2^)= Σ2 So, n=2 m=2 which is divergent is divergent So, by Cauchy Conden sation testn)- o as is divergeat So, applying comparison test is divergent On