Harsh Kumar

 11 Find the sum of first $n$ terms of the series: $\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots +\frac{1}{n\times(n+1)}$ 9 Why is the solution to $x-\sqrt 4=0$ not $x=\pm 2$? 7 What must be the simplest proof of the sum of first $n$ natural numbers? 6 Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction. 6 Find sum of numbers from $1-100$ which are not divisible by $3$ and$7$

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### Questions (15)

 30 Is every parallelogram a rectangle ?? 8 Prove that $\frac{x_1}{x_2}+\frac{x_2}{x_3}+\frac{x_3}{x_4}+\cdots +\frac{x_{n-1}}{x_n}+\frac{x_n}{x_1}<2n-1$ [closed] 6 What is the proof of divisibility by $13$? [duplicate] 4 Let $a,b,c$ be the length of sides of a triangle then prove that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge0$ [duplicate] 4 The largest value of $n$ such that $n+10| n^3+100$ [duplicate]

### Tags (65)

 41 algebra-precalculus × 19 12 radicals × 3 26 summation × 5 12 telescopic-series × 2 18 sequences-and-series × 5 9 circles × 3 14 geometry × 12 9 proof-writing × 2 13 quadratics × 7 7 elementary-number-theory × 10