Find the following:
$$\sum_{n=10}^{20}n^r$$

Question

Find the following:
$$\sum_{n=10}^{20}n^r$$

anonymous · Answer

what is r?

unklerhaukus · Answer

$$=10^r+11^r+12^r+13^r+14^r+15^r+16^r+17^r+18^r+19^r+20^r$$

kira_yamato · Answer

@FFM r is just a constant.
@UnkleRhaukus is there a certain algebraic expression to say this long stretch of numbers?

anonymous · Answer

Kira to answer your second quotient quotient "NO".

kira_yamato · Answer

Quotient quotient? But anyways, thanks you...

anonymous · Answer

question.*

anonymous · Answer

There could be an expression using  HarmonicNumber, do you want that? If yes then you might consider reading about it.

unklerhaukus · Answer

well you could write it as a sum , but that is the original expression in the question

blockcolder · Answer

If I remember correctly, there's an expression that can be used for any integer r. It has to do with Bernoulli numbers.

anonymous · Answer

blockcolder · Answer

Yeah, that one. In this case, you need to get $\Large \sum_{n=1}^{20}n^r-\sum_{n=1}^{10}n^r$ to get the desired sum.

kira_yamato · Answer

Thank you... ありがとうございます！！

blockcolder · Answer

Douitashimapellete. (Not sure with spelling lol)