There are several very useful expressions that expression the sum of powers of integers in terms of the range of summation.

Notice that the degree of the expression on the right hand side is one more than the terms of the left hand side, so that summing a polynomial sequence increases the degree by one.

The series is always finite so n is a finite number and the series has a finite number of terms to add.

There are no such simple expressions for sums of fractional or decimal powers.

The expressions above, and similar expressions, act as building blocks which enable expressions for the sum of any finite polynomial series to be formed.