# Thread: finding the series

1. ## finding the series

How do we calculate for a given n and k the value of $S_n=T_n+U_n$ where $T_n=1^k+2^k+3^k+..n^k$ and $U_n= 1^1+2^2+3^3+..n^n$
Is this some kind of series/is there any general formula to it ?
Thanks.

2. ## Re: finding the series

Originally Posted by pranay
How do we calculate for a given n and k the value of $S_n=T_n+U_n$ where $T_n=1^k+2^k+3^k+..n^k$ and $U_n= 1^1+2^2+3^3+..n^n$
Is this some kind of series/is there any general formula to it ?
It is true that $S_n = \sum\limits_{j = 1}^n {\left( {j^k + j^j } \right)}$.

But is that really what you are asking?

3. ## Re: finding the series

actually i intend to find $S_n +S_{n-1}-2S_{n-2}$