Question

WHAT IS REASON BEHIND IT THAT OF AN NUMBER IS HAVING THE POWER OF - 1 THEN RECIPROCAL IS TAKEN OF THAT NUMBER........ NO ANSWERS LIKE THAT IT IS A LAW OF EXPONENT... SPAM ANSWERS WILL BE REPORTED.........

Answer 1

suppose u have a number
let 2,and u want to find inverse of it
....
....
u can write it as
(1+1)^-1
OK......


now
according to binomial theorem
(
$(1 + x) {}^{ - 1} = 1 - x + {x}^{2} .....$
so when u will put put here x=1..
look u are getting
$(1 + 1) {}^{ - 1} = 1 - 1 + 1 - 1 + ... \\ rhs \: is \: gp \: with \: a = 1 \: and \: r = - 1 \\ = \frac{a}{1 - r} = \frac{1}{1 - ( - 1)} = \frac{1}{2} \\ so \\ (1 + 1) {}^{ - 1} = 2 {}^{ - 1} = \frac{1}{2}$
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