k-1-1-k-1-k-2-k-3-1-

Tinku Tara June 3, 2023 None 0 Comments

Question Number 4939 by Yozzii last updated on 24/Mar/16

Σ_(k=1) ^∞ ((((−1)^(k+1) k^2 )/(k^3 +1)))=?

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=? \\ $$

Commented by prakash jain last updated on 24/Mar/16

I think ratio test will show cnvergence.

$$\mathrm{I}\:\mathrm{think}\:\mathrm{ratio}\:\mathrm{test}\:\mathrm{will}\:\mathrm{show}\:\mathrm{cnvergence}. \\ $$

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