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## Homework Statement

determine whether the Ʃ n

^{4}/ e

^{n2}is convergent or divergent?

## Homework Equations

## The Attempt at a Solution

Using Root test:

lim of n

^{4/n}/ e

^{n}as n approaches infinity

But lim of n

^{4/n}as n approaches infinity = ∞

^{0}

So: Let N = lim of n

^{4/n}as n approaches infinity

and: ln N = lim of 4ln(n)/n as n approaches infinity = ∞/∞

By Lhopitals rule: ln N = lim 4/n as n approaches infinity = 0

thus ln N = 0 ; 1 = N

Therefore: lim of n

^{4/n}/ e

^{n}as n approaches infinity = 1/∞ = 0

thus CONVERGE?

Is this solution Ok?