Hard infinite serie

africam

New member
Joined
Jan 27, 2019
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4
hi guys, i can´t solve this, for what values from \(\displaystyle a\) is this serie convergent?
\(\displaystyle a \epsilon R\) (is a constant)

\(\displaystyle
\sum_{n=1}^{\infty} \sqrt[]{n+a} - \sqrt[4]{n^2+2n}

=
\)
 
hi guys, i can´t solve this, for what values from \(\displaystyle a\) is this serie convergent?
\(\displaystyle a \epsilon R\) (is a constant)

\(\displaystyle
\sum_{n=1}^{\infty} \sqrt[]{n+a} - \sqrt[4]{n^2+2n}

=
\)
OK, so you can't solve this. What have you tried? Where are you stuck? We are willing to help but we need to know what you need help with.
 
OK, so you can't solve this. What have you tried? Where are you stuck? We are willing to help but we need to know what you need help with.

I have tried diferent convergence test, i think that it can be solve with comparision test, but i can´t find a good serie for that comparision. it can´t be solve whit the integral test, because it is not decreasing. if you can find known serie for comparision it can help me a lot
 
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