query: Finding a function $f(x)$ that's equal to the series $\sum_{n=0}^\infty \frac{n}{n+1}x^n$
positive_passages.docid: 92665
positive_passages.text: Find a function for the infinite sum $\sum_{n=0}^\infty \frac{n}{n+1}x^n$
negative_passages.docid: 60104
negative_passages.text: Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
negative_passages.docid: 14883
negative_passages.text: Find $\sum_{n=1}^{\infty}$ $\frac{n^{2}}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\left(n+4\right)}$
negative_passages.docid: 50435
negative_passages.text: Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$
negative_passages.docid: 87910
negative_passages.text: Evaluate $\sum^\infty_{n=1} \frac{1}{n^4} $using Parseval's theorem (Fourier series)
negative_passages.docid: 9610
negative_passages.text: Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
negative_passages.docid: 57372
negative_passages.text: Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
negative_passages.docid: 17056
negative_passages.text: How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
negative_passages.docid: 36674
negative_passages.text: Summation of series $\sum_{n=1}^\infty \frac{n^a}{b^n}$?
negative_passages.docid: 92690
negative_passages.text: Infinite Series $\sum\limits_{n=0}^{\infty}\arctan(\frac{1}{F_{2n+1}})$
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 54661
negative_passages.text: How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$
negative_passages.docid: 135927
negative_passages.text: Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
negative_passages.docid: 79415
negative_passages.text: The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$
negative_passages.docid: 42216
negative_passages.text: Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$
negative_passages.docid: 105497
negative_passages.text: A function satisfying a series equation
negative_passages.docid: 16143
negative_passages.text: How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?