Abhra Abir Kundu
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 23 $xy=1 \implies$minimum $x+y=$? 19 Show that $2^n>1+n\sqrt{2^{n-1}}$ 18 Prove $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots+\frac{1}{\sqrt{n}} > 2\:(\sqrt{n+1} − 1)$ 16 17! mod 13, How do I do this without a calculator 10 proving a sum of binomial coefficients

### Reputation (6,645)

 +10 Show that $\rho(x,y) = |\sin(x)-\sin(y)|$ is not a metric on $\mathbb{R}$? +10 Number of non decreasing sequences of length $M$ +10 Find the probability density function of $Z = \max (X, Y ) \mbox{ and } Z=X+Y$ +10 Prove $n\mid \phi(2^n-1)$

### Questions (8)

 3 Linear Independence of an infinite set . 3 $n|(n-1)!$ for all composite numbers $n>4,n\in \mathbb{N}$ 2 Monotonicity in an interval 1 Funny Proof of $2=1$ [duplicate] 1 Existence of Matrix inverses depending on the existence of the inverse of the others..

### Tags (101)

 123 algebra-precalculus × 36 43 sequences-and-series × 20 71 discrete-mathematics × 16 40 linear-algebra × 41 70 real-analysis × 30 39 proof-writing × 8 63 calculus × 34 33 elementary-number-theory × 14 63 inequality × 19 28 combinatorics × 21

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