QJEEAdv15Macc5f: JEE Advanced 2015 Mathematics - Class 11 JEEAdv15Macc5f Solution: The coefficient of in the expansion of (1 + x) (1 + (1 + ) .... …

Given expression is

$E = (1 + x)(1 + {x^2})(1 + {x^3})......(1 + {x^{100}})$

Coefficient of x⁹ in E

= coefficient of x⁹ in $(1 + x)(1 + {x^2})(1 + {x^3})......(1 + {x^9})$

$\Rightarrow$ Terms containing x⁹

$= (1\,.\,{x^9} + {x^1}\,.\,{x^8} + {x^2}\,.\,{x^7} + {x^3}\,.\,{x^6} + {x^4}\,.\,{x^5} + {x^1}\,.\,{x^2}\,.\,{x^6} + {x^1}\,.\,{x^3}\,.\,{x^5} + {x^2}\,.\,{x^3}\,.\,{x^4})$

$\Rightarrow$ Term containing x⁹ is 8x⁹ in E $\Rightarrow$ Coefficient of x⁹ = 8.