query: What is the answer of series of $n+(n-1)+(n-2)+\cdots.+1$
positive_passages.docid: 22443
positive_passages.text: What's this equation called (one more each iteration, find total for given iteration)?
negative_passages.docid: 125148
negative_passages.text: Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
negative_passages.docid: 112374
negative_passages.text: Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
negative_passages.docid: 23726
negative_passages.text: A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
negative_passages.docid: 60902
negative_passages.text: Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
negative_passages.docid: 68853
negative_passages.text: Is there any formula for the series $1 + \frac12 + \frac13 + \cdots + \frac 1 n = ?$
negative_passages.docid: 57780
negative_passages.text: $\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
negative_passages.docid: 113189
negative_passages.text: Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
negative_passages.docid: 80432
negative_passages.text: Is the series convergent $x + x^{1+\frac{1}{2}}+x^{1+\frac{1}{2}+ \frac{1}{3}}+\cdots$
negative_passages.docid: 153409
negative_passages.text: Sum of $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{9}+\frac{1}{12}+\cdots$
negative_passages.docid: 86900
negative_passages.text: Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
negative_passages.docid: 53658
negative_passages.text: Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
negative_passages.docid: 22592
negative_passages.text: $1\cdot 3 + 2\cdot 4 + 3\cdot 5 + \cdots + n(n+2) = n(n+1)(2n+7)/6$ by mathematical induction
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: 92704
negative_passages.text: Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
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: 30895
negative_passages.text: Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$