Vidyamanohar

A place I would like to share some concepts, ideas, puzzles that simulate the minds of those interested in Math - for competitions or fun.

Monday, February 13, 2012

Puzzle 28 - Integration

Let ${\rm{f}}\left( {\rm{n}} \right)$ denotes the coefficient of ${{\rm{x}}^{{\rm{2}}0{\rm{12}}}}$ in the expansion of ${\left( {{\rm{1}} + {\rm{x}}} \right)^{\rm{n}}}$ . Then evaluate $\int\limits_0^1 {f( - t - 1)\left[ {\frac{1}{{t + 1}} + \frac{1}{{t + 2}} + \frac{1}{{t + 3}}...\frac{1}{{t + 2012}}} \right]} dt$