(x - \(\frac1{x^2}\))15 (Term of independent of x in (x - \(\frac1{x^2}\))15)
General term in the expansion of
(x - \(\frac1{x^2}\))15 is Tr+1 = 15Cr x15-r (\(-\frac1{x^2}\))r
= (-1)r 15Cr x15-r- 2r
= (-1)r15Cr x15-3r
For independent term of x, we have
15 - 3r = 0
⇒ r = 15/3 = 5
\(\therefore\) Independent term of x in (x - \(\frac1{x^2}\))15 is
T6 = (-1)5 15C5 = -15C5