Intuitively I would certainly say 0 however I desire to acquire a second opinion.We recognize that \$frac1n\$ approaches 0, as n goes to infinity.

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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\$ ? Thanks for contributing a solution to steustatiushistory.orgematics Stack Exchange!

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