In the expansion of ( x + 1 3 x ^2 )¹⁰ the value of constant term (independent of x ) is

Step-by-step solution

Let r ^ th term is independent of x . aligned & T_r= ^n C_r x^r y^ n-r & = ¹⁰ C_r( x )^r ( 1 3 x^2 )^ 10-r & = ¹⁰ C_r ( 1 3 )^ 10-r ( x )^r ( 1 x^2 )^ 10-r aligned Equating the coefficient of x to zero. aligned & x^ r / 2 x ^ -2(10- r ) = x ^0 & r 2 -20+2 r =0 & 5 2 r =20 r =8 aligned aligned Coefficient & = ¹⁰ C _ r ( 1 3 )^ 10- r & = ¹⁰ C ₈ ( 1 3 )¹⁰⁻⁸ aligned = 10 9 2 1 9 =5