Thursday, 5 December 2013

Why does this series divergent?



Can anyone explain me why does this serie diverge?!




$$\sum_{n=0}^\infty n^2 \sin\left(\dfrac n{n^4 + 1}\right)$$


Answer



sin(x) is like x when x tends to 0, so this is like the $\sum n^2 * 1 / (n^3)$ which is like $\sum 1/n$


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