1.

Find the coefficient of  x-2 in (x + \(\frac{1}{x^2}\))17

Answer»

Here, x → x, a → \(\frac{1}{x^2}\)and n = 17 

∴ Tr+1 = 17Cr.x17-r(\(\frac{1}{x^2}\))

Tr+1 = 17Cr.x17-r-2r 

= 17Crx17-3r 

To find the coefficient of x-2, equate the power of x to -2 

17 – 3r = -2 ⇒ 17 + 2 = 3r ⇒ 3r ⇒ r = \(\frac{19}{3}\)

Since r is a fraction the coefficient of x-2 is 0.



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