query: Sum of the series $\sum \frac{n}{2^{n}}$
positive_passages.docid: 17056
positive_passages.text: How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
negative_passages.docid: 104078
negative_passages.text: Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
negative_passages.docid: 117843
negative_passages.text: Finding the sum of series $\sum_{n=0}^∞ \frac{2^n + 3^n}{6^n}$
negative_passages.docid: 130548
negative_passages.text: What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?
negative_passages.docid: 70841
negative_passages.text: A simple series $\sum_{i=1}^\infty \frac{i}{2^i} = 2$
negative_passages.docid: 91458
negative_passages.text: Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$
negative_passages.docid: 18814
negative_passages.text: Sum of the series $1+\frac{1\cdot 3}{6}+\frac{1\cdot3\cdot5}{6\cdot8}+\cdots$
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: 22636
negative_passages.text: Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
negative_passages.docid: 61749
negative_passages.text: Limit of the infinite sum of $\frac{n}{2^n}$?
negative_passages.docid: 155611
negative_passages.text: Sum of series $\frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{4 \cdot 5 \cdot 6} + \frac{1}{6 \cdot 7 \cdot 8} + \cdots $
negative_passages.docid: 38760
negative_passages.text: Infinite Series $\sum\limits_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}$
negative_passages.docid: 49936
negative_passages.text: Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$
negative_passages.docid: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
negative_passages.docid: 17686
negative_passages.text: Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
negative_passages.docid: 32637
negative_passages.text: What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$
negative_passages.docid: 16967
negative_passages.text: Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$