Question: In expansion of (1 + x + x2 ................. + x27) (1 + x + x2 .....

Question

In expansion of (1 + x + x² ................. + x²⁷) (1 + x + x² ... + x¹⁴)², coefficient of x²⁸ is –

Answer 1

coefficent of x^r in (1 – x)^–n is ^n+r–1C_r

\ given product = $\frac { \left( 1 - x ^ { 28 } \right) } { ( 1 - x ) }$ $\left( \frac{1 - x^{15}}{1 - x} \right)^{2}$

= (1 – x²⁸) (1 – 2x¹⁵) (1 – x)^–3

\ Coefficient of x²⁸ in (1 – 2x¹⁵ – x²⁸)(1 – x)^–3 is

= ³⁰C₂ – 2.¹⁵C₂ –1= 224

Question: In expansion of (1 + x + x<sup>2</sup> ................. + x<sup>27</sup>) (1 + x + x<sup>2</sup> .....