Term independent of x in expansion of {(1 + x)^n}{left( {1 + frac{1}{x}} right)^n} is

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7.Binomial Theorem

hard

The term independent of $x$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is

A

$C_0^2 + 2C_1^2 + .... + (n + 1)C_n^2$

B

${({C_0} + {C_1} + .... + {C_n})^2}$

C

$C_0^2 + C_1^2 + ..... + C_n^2$

D

None of these

Solution

(c) As in Previous question, obviously the term independent of $x$ will be

$^n{C_0}{.^n}{C_0} + {\,^n}{C_1}{.^n}{C_1} + {…..^n}{C_n}{.^n}{C_n} = C_0^2 + C_1^2 + …. + C_n^2$.

Standard 11

Mathematics

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