query: Evaluate the sum $1-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+\frac{1}{5^2}+\ldots$
positive_passages.docid: 116723
positive_passages.text: Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
negative_passages.docid: 153989
negative_passages.text: How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?
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: 89367
negative_passages.text: Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
negative_passages.docid: 136444
negative_passages.text: Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
negative_passages.docid: 19868
negative_passages.text: Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
negative_passages.docid: 71824
negative_passages.text: Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$
negative_passages.docid: 47572
negative_passages.text: Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
negative_passages.docid: 94678
negative_passages.text: Evaluate $\sum\limits_{n=1}^{\infty} \frac{1}{2^n}\tan\frac{x}{2^n}$
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 84557
negative_passages.text: Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$
negative_passages.docid: 130083
negative_passages.text: Evaluating sum of a combination series
negative_passages.docid: 22505
negative_passages.text: Evaluate : $1+\frac{2}{6}+\frac{2\cdot 5}{6\cdot 12}+\frac{2\cdot 5\cdot 8}{6\cdot12\cdot 18}+\ldots$
negative_passages.docid: 112036
negative_passages.text: sum of series $\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms
negative_passages.docid: 36951
negative_passages.text: How to evaluate the series $1+\frac34+\frac{3\cdot5}{4\cdot8}+\frac{3\cdot5\cdot7}{4\cdot8\cdot12}+\cdots$
negative_passages.docid: 127806
negative_passages.text: How to find the sum of the series $\sum_{k=2}^\infty \frac{1}{k^2-1}$?
negative_passages.docid: 115420
negative_passages.text: Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$