16 How to solve this series: $\sum_{k=0}^{2n+1} (-1)^kk$ 11 Prove that $A(A+B)^{-1}B=B(A+B)^{-1}A$ 11 The function $f : \mathbb{R} \rightarrow \mathbb{R}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{R}$. Find $f(x)$. 10 Under what conditions is $AA^T$ invertible? 9 Evaluation of $\int x^{26}(x-1)^{17}(5x-3)dx$

### Reputation (9,014)

 +10 Under what conditions is $AA^T$ invertible? +10 Interpreting the Lindeberg's condition +10 Prove $|\int_{a}^{b}f(t)dt|\le \int_{a}^{b}|f(t)|dt$ complex +10 Squaring matrices and positive semidefiniteness

### Questions (112)

 15 Egg vs. chicken: trig functions, exponential, real and complex 9 Interpreting the Lindeberg's condition 8 Eigenvalues of $MA$ versus eigenvalues of $A$ for orthogonal projection $M$ 7 Generating correlated arbitrary random variables 6 Signing $y''$ from $\log(\frac{x+y}{x})=x+y$

### Tags (173)

 107 inequality × 45 45 elementary-number-theory × 16 68 linear-algebra × 64 42 number-theory × 12 62 algebra-precalculus × 37 41 probability × 65 61 matrices × 49 41 sequences-and-series × 12 56 calculus × 30 36 functions × 11

### Bookmarks (141)

 756 The staircase paradox, or why $\pi\ne4$ 191 Books on Number Theory for Layman [closed] 166 “Advice to young mathematicians” 121 What's your favorite proof accessible to a general audience? [closed] 89 Simplest or nicest proof that $1+x \le e^x$