query: Calculate the nature of the following series
positive_passages.docid: 145007
positive_passages.text: Two problems on real number series
negative_passages.docid: 145886
negative_passages.text: Power series representation/calculation
negative_passages.docid: 26491
negative_passages.text: Sum function of a series
negative_passages.docid: 93690
negative_passages.text: How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
negative_passages.docid: 58262
negative_passages.text: Find the sum of the series $1+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{5}\cdot\frac{1}{4^2}+\frac{1}{7}\cdot\frac{1}{4^3}+\cdots$
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: 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: 87976
negative_passages.text: How to solve these series?
negative_passages.docid: 122445
negative_passages.text: Sum of the series:$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\cdots$
negative_passages.docid: 67180
negative_passages.text: Manipulating infinite series
negative_passages.docid: 133073
negative_passages.text: Evaluating series with factorial denominator (sanity check).
negative_passages.docid: 70841
negative_passages.text: A simple series $\sum_{i=1}^\infty \frac{i}{2^i} = 2$
negative_passages.docid: 84121
negative_passages.text: Double factorial series
negative_passages.docid: 31731
negative_passages.text: How to turn this into an equation and then sum the series?
negative_passages.docid: 133420
negative_passages.text: Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
negative_passages.docid: 64076
negative_passages.text: how to show that this complex series converge?
negative_passages.docid: 53389
negative_passages.text: Consider the series $ ∑_{n=1}^∞ x^2+ n/n^2$ . Pick out the true statements: