# Sush

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# 136 Questions

 21 $\lfloor0.999\dots\rfloor= ?$ $0$ or $1$? 20 Prove that $\sqrt 2 +\sqrt 3$ is irrational. [duplicate] 7 Probability question: $100$ balls with $r$ red balls. 6 The value of $\binom{50}0\binom{50}1+\binom{50}1\binom{50}2+\dots+\binom{50}{49}\binom{50}{50}$ is 5 How to write $\frac{k}{k}$ using $\sum$ notation?

# 1,343 Reputation

 +5 Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$ +5 How are $Var(X)$ and $Var(X^2)$ both positive? +5 Show that $\sum_{r-k=0}^m\left(\sum_{k=0}^n\binom nk\binom{m}{r-k}x^r\right)=\sum_{r=0}^{m+n}\left(\sum_{k=0}^r\binom nk\binom{m}{r-k}\right)x^r$ +5 Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$

 1 How the inequality $\frac1{n+2} \leq \left|\frac{n!}{e}-!n\right|$ holds? 0 I'm stuck…please help probability questions

# 64 Tags

 1 combinatorics × 20 0 optimization × 8 0 probability × 20 0 matrices × 5 0 real-analysis × 11 0 sequences-and-series × 5 0 linear-algebra × 11 0 summation × 5 0 calculus × 10 0 limits × 4

# 2 Accounts

 Mathematics 1,343 rep 418 Cross Validated 189 rep 5