Find $n$ such that the $10th$ term of the binomial expansion $(5+n)^n$ to be the greatest term.
I know that when $n$ is given i would take the ratio $\frac{T_{k+2}}{T_{k+1}}$ and compare it to 1 so i could find the greatest term. But now with n being an unkown i do not really get anything useful.
Then i tried using the ratio $\frac{T_{10}}{T_{k+1}}$ and compare it to 1 but again i did not know how to find $n$ from here.
What do you suggest ?
Thanks in advance!