# Sum of a series of a number raised to incrementing powers— for any number

Sum of a series of a number raised to incrementing powers. I have a sub question on this. As I dont have reputation to ask for in comment. The formula being derived for series of summation of powers to 2 i.e $$2^{n+1}-1$$ doesnt apply for other numbers suppose $$5^0+5^1+5^2+5^3+5^4$$ is not equal to $$5^{4+1}-1$$. Hence I request if there is any generalized formula i.e that will give the summation of series of powers of the number available.

If any such formula is available need your help!!

$$S=5^0+5^1+5^2+5^3+5^4+\cdots+5^n$$ $$5S=5^1+5^2+5^3+5^4+5^5+\cdots+5^{n+1}$$ $$4S=5^{n+1}-1$$ $$S=\frac{5^{n+1}-1}{4}$$
In general to find $$1+x+x^2+\cdots+x^n$$, $$\sum_{j=0}^{n}x^j=\frac{x^{n+1}-1}{x-1}$$