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Partial Sum of a Polynomial [duplicate]

Possible Duplicate: why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ I'm searching for a way to find the partial sum of a polynomial, is there any way of doing this ...
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Possible Duplicate: why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ If I want to find the formula for $$\sum_{k=1}^n k^2$$ I would do the next: $$(n+1)^2 = a(n+1)^3 + b(n+... 3answers 460 views Evaluating N-th partial sums of polynomials [duplicate] Possible Duplicate: why is \sum\limits_{k=1}^{n} k^m a polynomial with degree m+1 in n How can I find \sum_{n=1}^N n^2-n? Wolfram Alpha will tell you that it is \frac{N}{3} (N-1)(N+1), ... 3answers 161 views Finite summation [duplicate] Possible Duplicate: why is \sum\limits_{k=1}^{n} k^m a polynomial with degree m+1 in n What is the proof without induction for : (1) \sum_{i=1}^n\ i^2= \frac{n(n+1)(2n+1)}{6} (2) \... 1answer 210 views Formula for \sum_{k=1}^{n}{k^p} where p is a positive integer [duplicate] Possible Duplicate: why is \sum\limits_{k=1}^{n} k^m a polynomial with degree m+1 in n Any hints that can take me from here or am I completely lost. \sum_{k=1}^{n}{k^p}=\sum_{a=1}^{p}(-1)^... 2answers 94 views Finding an expression for the sum of n tems of the series 1^2 + 2^2 + 3^2 + … + n^2 [duplicate] Possible Duplicate: why is \sum\limits_{k=1}^{n} k^m a polynomial with degree m+1 in n I know that if you have a non-arithmetic or geometric progression, you can find a sum S of a series ... 0answers 79 views Sum of series: 1^k+2^k+3^k+…+n^k =? [duplicate] Is there any better algorithm to solve this equation other than brute force. 1^k+2^k+3^k+...+n^k= formula? Here k is a natural number, n is a natural number. 31answers 61k views Sum of First n Squares Equals \frac{n(n+1)(2n+1)}{6} I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:$$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$I really ... 4answers 376 views Formula for 1^2+2^2+3^2+…+n^2 In example to get formula for 1^2+2^2+3^2+...+n^2 they express f(n) as:$$f(n)=an^3+bn^2+cn+d$$also known that f(0)=0, f(1)=1, f(2)=5 and f(3)=14 Then this values are inserted into ... 1answer 6k views How to calculate  1^k+2^k+3^k+\cdots+N^k  with given values of N and k? [duplicate] Here  1<N<10^9 and 0<k<50 So we have to calculate it in order of O(\log N). 2answers 967 views Conceptual basis for formula for sum of n first integers raised to power k, Most programmers (including me) are painfully aware of quadratic behavior resulting from a loop that internally performs 1, 2, 3, 4, 5 and so on operations per iteration,$$\sum_{i=1}^n i = \frac{n \...
$$1^2+2^2+3^2+...+10000$$ How do you find the exact value of that? I'm studying induction, and I'm still not sure how to get that value.