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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!!

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This is a geometric series

$$S=5^0+5^1+5^2+5^3+5^4+\cdots+5^n$$ $$5S=5^1+5^2+5^3+5^4+5^5+\cdots+5^{n+1}$$ $$4S=5^{n+1}-1$$ $$S=\frac{5^{n+1}-1}{4}$$

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

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  • $\begingroup$ May I know how are you deriving step3 from step2 from your answer I dont understand $\endgroup$ – Naseer Mohammad Dec 22 '18 at 9:15
  • $\begingroup$ Step 3 is just Step 2 - Step 1 $\endgroup$ – Sik Feng Cheong Dec 22 '18 at 9:15
  • $\begingroup$ Great!! Correct Thank you.Very weak in Maths $\endgroup$ – Naseer Mohammad Dec 22 '18 at 9:17

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