query: How to find $\sum_{i=1}^{\infty} 0.5^i \cdot i^2$?
positive_passages.docid: 61547
positive_passages.text: Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$
negative_passages.docid: 92810
negative_passages.text: What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
negative_passages.docid: 129734
negative_passages.text: Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
negative_passages.docid: 114031
negative_passages.text: Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
negative_passages.docid: 78542
negative_passages.text: What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
negative_passages.docid: 98933
negative_passages.text: Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
negative_passages.docid: 6416
negative_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 138313
negative_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
negative_passages.docid: 52177
negative_passages.text: divergence/convergence $\sum_{k=1}^{\infty} \frac{1}{5k+2}$
negative_passages.docid: 7
negative_passages.text: Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
negative_passages.docid: 22657
negative_passages.text: How to find the sum of the infinite series?
negative_passages.docid: 28378
negative_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
negative_passages.docid: 17686
negative_passages.text: Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
negative_passages.docid: 70841
negative_passages.text: A simple series $\sum_{i=1}^\infty \frac{i}{2^i} = 2$
negative_passages.docid: 124002
negative_passages.text: How prove this series $\sum_{n=1}^{\infty}\frac{e^n\cdot n!}{n^n}$ divergent
negative_passages.docid: 88973
negative_passages.text: How do you calculate this sum $\sum_{n=1}^\infty nx^n$?
negative_passages.docid: 63900
negative_passages.text: Convergent or divergent series: $\sum_{n=1}^{\infty} \sqrt{a_n \cdot a_{n+1}}$?