If = 5 2 ! 3 + 5 7 3 ! 3^2 + 5 7 9 4 ! 3^3 + , then ^2+4 is equal to

Step-by-step solution

Given that, = 5 2 ! 3 + 5 7 3 ! 3^2 + 5 7 9 4 ! 3^3 + We know that, aligned (1+x)^n= & 1+ n x 1 ! + n(n-1) 2 ! x^2 & + n(n-1)(n-2) 3 ! x^3+ aligned On comparing Eqs. (i) and (ii), with respect to factorial aligned n(n-1) x^2 & = 5 3 n(n-1)(n-2) x^3 & = 5 7 3^2 aligned and n(n-1)(n-2)(n-3) x^4= 5 7 9 3^3 On dividing Eq. (iv) by (iii) and Eq. (v) by (iv), we get (n-2) x= 7 3 and (n-3) x=3 Again, dividing Eq. (vi) by (vii), we get array rlrl & & n-2 n-3 & = 7 9 & & 9 n-18 & =7 n-21 & & 2 n & =-3 & n & =- 3 2 array On