query: Evaluate the sum $1+2+3+...+n$
positive_passages.docid: 2675
positive_passages.text: Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
negative_passages.docid: 142994
negative_passages.text: How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
negative_passages.docid: 64581
negative_passages.text: How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
negative_passages.docid: 89367
negative_passages.text: Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 87589
negative_passages.text: Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
negative_passages.docid: 152588
negative_passages.text: Expression for $n+n(n-1)+n(n-1)(n-2)+...+n!$
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: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 122534
negative_passages.text: Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
negative_passages.docid: 94143
negative_passages.text: Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $
negative_passages.docid: 13085
negative_passages.text: Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
negative_passages.docid: 83145
negative_passages.text: Sum of rational numbers
negative_passages.docid: 47706
negative_passages.text: Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
negative_passages.docid: 54604
negative_passages.text: Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
negative_passages.docid: 62271
negative_passages.text: Find the sum of the series: $\cos^3 \alpha +\cos^3 {3\alpha} + \cos^3 {5\alpha}+....+\cos^3 {(2n-1)\alpha}$.
negative_passages.docid: 7302
negative_passages.text: $\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?