Find the coefficient of x5 in (x + \(\frac{1}{x^2}\))17 – InterviewSolution

InterviewSolution

1.

Find the coefficient of x5 in (x + \(\frac{1}{x^2}\))17

Answer»

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

T_r+1 = ¹⁷C_r.x^17-r(\(\frac{1}{x^2}\))^r

= ¹⁷C_rx^17-3r

To find the coefficient of x⁵, equate the power of x to 5

∴ 17 – 3r = 5

12 = 23 ⇒ r = 4

T₄₊₁ = T₅ = ¹⁷C₄.x⁵

∴ The coefficient of x⁵ is ¹⁷C₄

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