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Find the Co-efficient of x^{11} in the expansion of `(x + 2/x^2)^17`

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#### Solution

In `(x + 2/x^2)^17`, n = 17, x = x, a = `2/x^2`

∴ The general terms is

`"t"_(r + 1) = n"C"_r x^(n - r) a^r`

`= 17C_r x^(17-r) (2/x^2)^r`

`= 17C_r x^(17-r) * 2^r/(x^(2r))`

`= 17C_r * 2^r x^(17 - 3r)` ....(1)

To get the co-efficient of x^{11},

⇒ 17 - 3r = 11

⇒ 17 - 11 = 3r

⇒ 3r = 6

⇒ r = 2

Put r = 2 in (1) we get,

`"t"_3 = 17"C"_2 2^2 x^(17-3(2))`

= 17C_{2}(4)x^{11}

`= (17 xx 16)/(2xx1) xx 4 * x^11`

= 544 x^{11}

∴ Co-efficient of x^{11} is 544.

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