# Sum of powers of integers

#### eljose

Let,s suppose we want to do this sum:

$$1+2^{m}+3^{m}+............+n^{m}$$ n finite

then we could use the property of the differences:

$$\sum_{n=0}^{n}(y(k)-y(k-1))=y(n)-y(0)$$

so for any function of the form f(x)=x^{m} m integer you need to solve:

$$y(n)-y(n-1)=n^{m}$$ i don,t know how to solve

it.. i have tried the ansatz y(n)=K(n) with K(n) a Polynomial of degree m+1 but i don,t get the usual results for the sum..could someone help?..

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