How do I prove that $\sum^n_{i=1}(x_i -\bar{x})(y_i - \bar{y}) = \sum^n_{i=1}(x_i -\bar{x})y_i^*$
67454
Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^n (x_i - \bar{x})(y_i)$.
119628
Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
131771
Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$
62504
Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
14968
How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$
133076
Prove this sum equal to an expression.
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
15164
Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
16177
Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
16776
How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$