15 questions linked to/from Finite Sum of Power?
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### How to get to the formula for the sum of squares of first n numbers? [duplicate]

Possible Duplicate: How do I come up with a function to count a pyramid of apples? Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? Finite Sum of Power? I know that the sum of ...
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### Formula for partial sum of Riemann zeta function [duplicate]

Possible Duplicate: Finite Sum of Power? Suppose $f(s,k) = \sum_{n=1}^k n^{-s}$ is the Riemann zeta function truncated at the k-th term. I read on mathoverflow that there is a formula for $f(s,k)$...
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Apologies for the confusing title but I couldn't think of a better way to phrase it. What I'm talking about is this: $$\sum_{i=1}^n \;i = \frac{1}{2}n \left(n+1\right)$$ $$\sum_{i=1}^n \; \frac{1}{... 1answer 6k views ### How to calculate  1^k+2^k+3^k+\cdots+N^k  with given values of N and k? [duplicate] Here  1<N<10^9 and 0<k<50 So we have to calculate it in order of O(\log N). 4answers 441 views ### Summation of n-squared, cubed, etc. [duplicate] How do you in general derive a formula for summation of n-squared, n-cubed, etc...? Clear explanation with reference would be great. 2answers 195 views ### Evaluating \sum_{k=1}^n k^x [duplicate] Possible Duplicate: Finite Sum of Power? Is there a general expression for \sum_{k=1}^n k^x for any integer value of x? The table for x=1,2,\dots 10 is given here. Is there formula for any ... 2answers 112 views ### How can i find summation of the series i^k [duplicate] Series :$$\sum_{i =1}^{n} i^k= 1^k+ 2^k + 3^k + 4^k +\ldots+n^k$$where k is a constant. This does not seem to be Geometric progression , how can I evaluate the sum? If possible if also want to ... 13answers 4k views ### Methods to compute \sum_{k=1}^nk^p without Faulhaber's formula As far as every question I've seen concerning "what is \sum_{k=1}^nk^p" is always answered with "Faulhaber's formula" and that is just about the only answer. In an attempt to make more interesting ... 2answers 5k views ### Sum of perfect squares to infinity In this article, the method of computing 1+2+\dots is outlined. Is there a similar method for computing 1^2+2^2+\dots? What about for the general power n? (That is, 1^n+2^n+\dots) 2answers 2k views ### How to calculate the sum of (n-1)^2+(n-2)^2+…+1? [closed] How to calculate the sum of the following series?$$(n-1)^2+(n-2)^2+...+1$$Thank you in advance 4answers 1k views ### how can one find the value of the expression, (1^2+2^2+3^2+\cdots+n^2) [duplicate] Possible Duplicate: Proof that \sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}? Summation of natural number set with power of m How to get to the formula for the sum of squares of first n ... 2answers 388 views ### Has anyone noticed this pattern? I've been messing around a bit and I noticed a curious pattern when it comes to progressions of powers. Let's take the progression of consecutive integers: 1,2,3,4,5,6,7,... Obviously it's an ... 3answers 90 views ### Basic Mathematical Induction [duplicate] I'm not quite sure how to approach this question. I need to prove that for$$n\ge11^2+2^2+3^3+\dots+n^2=\frac16n(n+1)(2n+1)$$Do I just plug 1 and see if$$\frac16(1)((1)+1)(2(1)+1) = 1^2\...
I am curious about whether a closed form expression of $$\sum_{k=1}^{n}k^\alpha$$ for $\alpha \in \mathbb{R}$ exists in terms of special functions. Clearly for the natural number case we have the ...
Among other similarities, why is that in every $S_{ a }=\sum _{ j=1 }^{ n }{ { j }^{ a } }$ the denominator is the product of the sum of the coefficients of powers of n of individual factors? \$ S_{ 1 ...