Prove that,
$\left[ x \right] + \left[ {x + \frac{1}{n}} \right] +......... + \left[ {x + \frac{{n - 1}}{n}} \right] = \left[ {nx} \right]$
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$