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

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

• Very much worth checking this at the beginning. It will become second nature before long, but people who get the ideas concretely in their heads remember them better, and use them more effectively. – Mark Bennet May 7 at 20:14

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.
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