(2^{n})can be expanded by binomial theorem, if. | MATH - EXPANSION OF BINOMIAL THEOREM | SolveeIt

$2^{n}$ can be expanded by binomial theorem, if.

$n.2^{n - 1}$

$n.2^{n + 1}$

$\frac{C_{0}}{1} + \frac{C_{2}}{3} + \frac{C_{4}}{5} + \frac{C_{6}}{7} + ....$

$\frac{2^{n + 1}}{n + 1}$

Answer

$\frac{C_{0}}{1} + \frac{C_{2}}{3} + \frac{C_{4}}{5} + \frac{C_{6}}{7} + ....$

Explanation

The given expression can be written as

$(1 + x + x^{2} + ...)^{- n} = \lbrack(1 - x)^{- 1}\rbrack^{- n} = (1 - x)^{n}$ and it is valid only when

$=^{n}C_{0} -^{n}C_{1}x +^{n}C_{2}x^{2} + ... + ( - 1{)^{n}}^{n}C_{n}.x^{n}$ .

Question: \(2^{n}\)can be expanded by binomial theorem, if....