If x= 1.3 3 6 + 1 3 5 3 6 9 + 1 3 5 7 3 6 9 12 + to infinite terms, then 9 x^2+24 x=

Step-by-step solution

Given that, aligned x & = 1 3 3 6 + 1 3 5 3 6 9 + 1 3 5 7 3 6 9 12 + terms x & = 1 3 3^2(2 !) + 1 3 5 3^3(3 !) + 1 3 5 7 3^4(4 !) + terms aligned aligned x= & 1 2 ( 1 2 +1 ) 2 ! ( 2 3 )^2 & + ( 1 2 ) ( 1 2 +1 ) ( 1 2 +2 ) 3 ! ( 2 3 )^3+ x= & [1+ 1 2 ( 2 3 )+ 1 2 ( 1 2 +1 ) 2 ! ( 2 3 )^2 . & .+ 1 2 ( 1 2 +1 ) ( 1 2 +1 ) 3 ! ( 2 3 )^3 . ]- (1+ 1 3 ) aligned Now, by using binomial expansion for any index aligned & x= (1- 2 3 )^ -1 / 2 - 4 3 x= ( 1 3 )^ -1 / 2 - 4 3 & x= 3 - 4 3 3 x+4=3 3 aligned On squaring both the s