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प्रश्न
Find the Co-efficient of x11 in the expansion of `(x + 2/x^2)^17`
उत्तर
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 x11,
⇒ 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))`
= 17C2(4)x11
`= (17 xx 16)/(2xx1) xx 4 * x^11`
= 544 x11
∴ Co-efficient of x11 is 544.
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