Question

approximate value formula in binomial theorem

Answer 1

HEY DEAR HERE IS YOUR ANSWER  ^_^

The binomial approximation is useful for approximately calculating powers of sums of a small number and 1. It states that if {\displaystyle |x|<1} and {\displaystyle |\alpha x|} ≪ {\displaystyle 1} where {\displaystyle x} and {\displaystyle \alpha } are real or complex numbers, then

{\displaystyle (1+x)^{\alpha }\approx 1+\alpha x.}

If either {\displaystyle x} or {\displaystyle \alpha } are complex then the absolute value denotes the modulus of the complex number.

The benefit of this approximation is that {\displaystyle \alpha } is converted from a power to multiplicative factor. This can greatly simplify mathematical expressions (see example) and is a common tool in physics.[1]

This approximation can be proven several ways including the binomial theorem and ignoring the terms beyond the first two.

I HOPE THIS WILL HELP YOU OUT.....

HAVE A GOOD DAY DEAR.....       ^_^