query: How to find the closed form for $\sum_{i=1}^k 3^{-i}$
positive_passages.docid: 16320
positive_passages.text: confused about geometric series closed formula
negative_passages.docid: 326
negative_passages.text: Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
negative_passages.docid: 20317
negative_passages.text: Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
negative_passages.docid: 115433
negative_passages.text: Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
negative_passages.docid: 92754
negative_passages.text: Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
negative_passages.docid: 81589
negative_passages.text: Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
negative_passages.docid: 87479
negative_passages.text: Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
negative_passages.docid: 101908
negative_passages.text: Solving summations of form $\sum_{i=0}^{\infty} i^kx^i$ without Differentiation and Integration
negative_passages.docid: 70390
negative_passages.text: is there a closed form expression for the following matrix infinite series
negative_passages.docid: 110262
negative_passages.text: Finding a closed formula for $1\cdot2\cdot3\cdots k +\dots + n(n+1)(n+2)\cdots(k+n-1)$
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: 75457
negative_passages.text: How do i simplify the following: $\sum_{i=1}^n (3i^2+4) - \sum_{j=2}^{n+1} (3j^2+1)$
negative_passages.docid: 47706
negative_passages.text: Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
negative_passages.docid: 69045
negative_passages.text: Solving this summation: $\sum_{i=1}^k i\cdot2^i$
negative_passages.docid: 89698
negative_passages.text: Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
negative_passages.docid: 123955
negative_passages.text: How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
negative_passages.docid: 16967
negative_passages.text: Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$