Is $\sum_{j=1}^{5}j^k=1^k+2^k+3^k+4^k+5^k$?

Question

Is $\sum_{j=1}^{5}j^k=1^k+2^k+3^k+4^k+5^k$. I wonder whether I construe it right...

Answer 1

Yes, that is correct, as $j$ is the index of your summation.

An argument could be made that you could simplify this by noting $1^k = 1$ but that's a minor thing. As-is, this is still correct.

Answer 2

Yes it is right. You just substitute every integer value from 1 to 5 in $j^k$ in place of j and add them up