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(1+x)^-2 = ? Explain it. ------------------------------

(1+x)^-2 = ?
Explain it.
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Grade:10

1 Answers

Arun
25750 Points
5 years ago

binomial expansion of(1+x)^n , where n is a negative power,

(1+x)^-2 = 1+nx +n(n-1)x^2/2! +n(n-1)(n-2)x^3/3! +… an infinite series true for |x| less than 1.

=1+(-2)x +(-2)(-3)x^2/2! +(-2)(-3)(-4)x^3/3! +…

=1–2x +3x^2 -4x^3 +…

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