for (1+x)^-n = 1 - nx +n(n+1)/2! - n(n+1)(n+2)/3!
for (1+x)^-3= 1 - 3x + 6x²- 10x³
now putting x as 2
(1+2)^-3 = 1 - 3(2) + 6(4) -10(8)
= 1-6+24-80
= -61
but 3^-3is 1/27 which is not -61.
please tell me why the difference.

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Solution

The rule for expansion of (1+x)^n says that second term of expansion which is |x| (mod x) has to be less than 1 .in Ur case it's 2 so it's not lesser than 1 thus leading u to get the incorrect answer.

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