query: what is the value of $\sum_{i=1}^ni^m$
positive_passages.docid: 50050
positive_passages.text: A formula for the power sums: $1^n+2^n+\dotsc +k^n=\,$?
negative_passages.docid: 103572
negative_passages.text: Does $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$ occur here?
negative_passages.docid: 54604
negative_passages.text: Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
negative_passages.docid: 3414
negative_passages.text: Value of Summation of $\log(n)$
negative_passages.docid: 30472
negative_passages.text: Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
negative_passages.docid: 115170
negative_passages.text: What is the formula for this numerical series?
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 111602
negative_passages.text: Help with telescoping sum $\sum_{i=3}^n \frac{1}{i(i+3)} $
negative_passages.docid: 3356
negative_passages.text: Why $\sum_{k=0}^m x^k $ is equal to $\dfrac{x^{m+1}-1}{x-1} $?
negative_passages.docid: 54753
negative_passages.text: What does $\sum_{i=1}^{10} 2$ mean exactly?
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: 26446
negative_passages.text: Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
negative_passages.docid: 83400
negative_passages.text: Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $
negative_passages.docid: 5332
negative_passages.text: Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
negative_passages.docid: 75457
negative_passages.text: How do i simplify the following: $\sum_{i=1}^n (3i^2+4) - \sum_{j=2}^{n+1} (3j^2+1)$
negative_passages.docid: 17453
negative_passages.text: What is sum of $\sum_{x=1}^n x \log (x)$
negative_passages.docid: 69045
negative_passages.text: Solving this summation: $\sum_{i=1}^k i\cdot2^i$