# does the series converge or diverge n=1 e^n/1+e^2n?

n=1 e^n/1+e^2n thanx

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• 8 years ago

Do you really mean a series? If you mean the series

Σ eⁿ/(1 + e^(2n)),

n=1

then yes it is convergent. If you do a limit comparison test to the convergent geometric series Σ 1/eⁿ, you get

lim (eⁿ/(1 + e^(2n))/(1/eⁿ) = 1.

n->∞

As this limit is positive and finite, both series converge or both series diverge. The series Σ 1/eⁿ is known to be convergent, so your series is also convergent.

You can also use the integral test, or direct comparison, or some other test.