You are watching: Sum of 1/sqrt(n)

We additionally know that $sum^infty_n=0frac1n$ diverges.We additionally know that $sum^infty_n=0frac1sqrtn$ diverges by the integral test and "straight comparison" test.

How have the right to we conclude anypoint around the limit from this knowledge around the limit of $frac1sqrtn$ ?

When I plot it I deserve to view it approaching zero yet how can I proove it ?

Just usage that $sqrtcdot$ is constant at $0$ and also $lim_n o infty frac1n = 0$. Then we acquire $$lim_n o infty frac1sqrtn = sqrtlim_n o infty frac1n = sqrt0 = 0.$$

From the divergence of $sum^infty_n=0frac1sqrtn$ we deserve to deduce nopoint, but:

$frac1sqrtn=|frac1sqrtn-0| frac1epsilon^2$.

Can you currently view that $frac1sqrtn o 0$ for $n o infty$ ?

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