query: Calculation of sums using Fourier series
positive_passages.docid: 148940
positive_passages.text: $\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$ by Fourier series of $x^2$
negative_passages.docid: 141978
negative_passages.text: How to find the infinite sum
negative_passages.docid: 103347
negative_passages.text: combinatorial proof of summation
negative_passages.docid: 143112
negative_passages.text: Series Summation,Convergence
negative_passages.docid: 131080
negative_passages.text: Geometric representation of the sum of a Geometric Series
negative_passages.docid: 51146
negative_passages.text: Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$
negative_passages.docid: 91784
negative_passages.text: Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 134610
negative_passages.text: Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
negative_passages.docid: 138492
negative_passages.text: Finding the sum of the infinite series whose general term is not easy to visualize: $\frac16+\frac5{6\cdot12}+\frac{5\cdot8}{6\cdot12\cdot18}+\cdots$
negative_passages.docid: 37771
negative_passages.text: Sum of a power series $n x^n$
negative_passages.docid: 148143
negative_passages.text: Find the sum to n terms as well as the sum to infinity of the series:
negative_passages.docid: 14884
negative_passages.text: Compute a sum with partial fraction decomposition and generating functions
negative_passages.docid: 30895
negative_passages.text: Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$
negative_passages.docid: 155250
negative_passages.text: Summation Series for fractions
negative_passages.docid: 130083
negative_passages.text: Evaluating sum of a combination series
negative_passages.docid: 155367
negative_passages.text: summation of multiplying series with negative terms