Question

Find the 4^th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`

Answer 1

Since r^th term from the end in the expansion of (a + b)ⁿ is (n – r + 2)^th term from the beginning.

Therefore 4^th term from the end is 9 – 4 + 2

i.e., 7^th term from the beginning

Which is given by T₇ = `""^9"C"_6 (x^3/2) ((-2)/x^2)^6`

= `""^9"C"_3 x^9/8 * 64/x^12`

= `(9 xx 8 xx 7)/(3 xx 2 xx 1) xx 64/x^3`

= `672/x^3`