query: Derive $\sum i^2$ without knowing the answer first
positive_passages.docid: 146333
positive_passages.text: Gaussian proof for the sum of squares?
negative_passages.docid: 84213
negative_passages.text: How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$
negative_passages.docid: 150642
negative_passages.text: How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
negative_passages.docid: 77486
negative_passages.text: What is the value of $i^i$?
negative_passages.docid: 16776
negative_passages.text: How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$
negative_passages.docid: 133076
negative_passages.text: Prove this sum equal to an expression.
negative_passages.docid: 105590
negative_passages.text: How to find sum of power series $\sum_{n=0}^\infty\frac{1}{n!(n+2)}$ by differentiation and integration?
negative_passages.docid: 39659
negative_passages.text: Is there a closed formula for this summation?
negative_passages.docid: 97266
negative_passages.text: Summation by parts (finite calculus) of $\sum\limits_{i=0}^{n}i\cdot a^i$
negative_passages.docid: 14968
negative_passages.text: How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$
negative_passages.docid: 99676
negative_passages.text: Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
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: 69478
negative_passages.text: Deducing a $\cos (kx)$ summation from the $e^{ikx}$ summation
negative_passages.docid: 137249
negative_passages.text: find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
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: 69045
negative_passages.text: Solving this summation: $\sum_{i=1}^k i\cdot2^i$
negative_passages.docid: 145274
negative_passages.text: Prove by induction $\sum \frac {1}{2^n} < 1$