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 ...