query: Formula to obtain sum of $ 1^k+2^k+3^k+\cdots+(n-1)^k+n^k$
positive_passages.docid: 45084
positive_passages.text: How is Faulhaber's formula derived?
negative_passages.docid: 121554
negative_passages.text: Finding $\sum\frac{1}{2^n(n+1)}$
negative_passages.docid: 151085
negative_passages.text: Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
negative_passages.docid: 30851
negative_passages.text: Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
negative_passages.docid: 126105
negative_passages.text: Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
negative_passages.docid: 134311
negative_passages.text: How to determine equation for $\sum_{k=1}^n k^3$
negative_passages.docid: 68848
negative_passages.text: How to simplify $\sum_{k=1}^nk\cdot k!$
negative_passages.docid: 146746
negative_passages.text: A formula for the sum of the triangular numbers?
negative_passages.docid: 69045
negative_passages.text: Solving this summation: $\sum_{i=1}^k i\cdot2^i$
negative_passages.docid: 102524
negative_passages.text: $ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?
negative_passages.docid: 94060
negative_passages.text: Sum of square binomial coefficients
negative_passages.docid: 29524
negative_passages.text: Formula for the sum $\sum_{i=2}^{n} \frac1{i^2-1}$
negative_passages.docid: 3798
negative_passages.text: Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
negative_passages.docid: 36361
negative_passages.text: How to calculate the summation $(\sum_{p = k}^{n} \binom{n}{p}) / 2^n$ quickly?
negative_passages.docid: 39909
negative_passages.text: Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
negative_passages.docid: 113189
negative_passages.text: Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $