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!!


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

  • $\begingroup$ 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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