Find the value of $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+...+\sqrt{1+\frac{1}{1999^2}+\frac{1}{2000^2}}$
62463
A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
104542
Evaluate $\frac{1}{3}+\frac{1}{4}\frac{1}{2!}+\frac{1}{5}\frac{1}{3!}+\dots$
143236
$ S_{n}=\frac{x}{x+1}+\frac{x^2}{(x+1)(x^2+1)}+...........+\frac{x^{2^{n}}}{(x+1)(x^2+1)...(x^{2^{n}}+1)}$
29190
$\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$
82317
Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$
150581
How do I show that $\frac a{1 - a^2} + \frac b{1 - b^2} + \frac c{1 - c^2} \ge \frac {3 \sqrt 3}2$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
60774
Find the value of : $\cos x \cos 2x...\cos 999x$ given that $x=\frac {2\pi}{1999}$
74434
Find expected value of $\frac{1}{1+\xi}$
128091
Find the range of possible values of $\sqrt{a^2+a+1}-\sqrt{a^2-a+1}$
57736
Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$
84159
The sum to n terms of the series $\frac{1}{\sqrt 1+\sqrt 3} + \frac{1}{\sqrt 3 +\sqrt 5} ....$
62758
How find this value $\frac{a^3}{(a-p)(a-q)}+\frac{b^3}{(b-p)(b-q)}+\frac{c^3}{(c-p)(c-q)}$
100995
For what $x$ : $2\sqrt{x}+\dfrac{1}{\sqrt{x+1}} \leq 2\sqrt{x+1}$
32355
How to find the sum of the sequence $\frac{1}{1+1^2+1^4} +\frac{2}{1+2^2+2^4} +\frac{3}{1+3^2+3^4}+.....$
124248
$1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$
17168
Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$