Question

Find $a$ and $b$ so that the $n^{th}$ term in the expansion of $\frac{a+bx}{{(1-x)}^2}$ may be $(3n-2)x^{n-1}$.

Answer 1

To Find the a and b so that the $n^{th}$ term in the expansion of $\frac{a+bx}{(1-x{)}^2}$ may be $(3n-2)x^{n-1}$

Let's Start this by Putting n = 1 , 2 ,3 ........

Successively We see that the Required Expansion will have Coefficients 1, 4, 7, 10........... ; that is

$a+bx={(1-x)}^2(1+4x+7x^2+10x^3+.....)$

$\therefore$ By Equating Coefficients

$a=1,b=4-2=2$

Hence ,

$a=1,b=2$