In the expansion of (1+x)⁴³ , if the coefficients of (2 r+1)^ th and ( r +2)^ th terms are equal, then what is the value of r ( r 1) ?

Step-by-step solution

Given, in the expansion g (1+ x )⁴³ , coefficients of (2 r +1)^ th term and ( r +2)^ th term are equal. Coefficient of (2 r +1)^ th term = ^ n C _ 2 r Coefficient of ( r +2)^ th term = n _ C _ r +1 aligned & n _ C _ 2 r = n _ C _ r +1 & 43_ C _ 2 r =43_ C _ r +1 ( n =43) & 2 r + r +1=43 & 3 r +1=43 & 3 r +42 r =14 aligned