1C0+3C2+5C4+7C6.....=

1Co+3C2+5C4+7C6.....1+3!n×(n−1) +5n×(n−1)(n−2)(n−3) +......n+11[(n+1)3!(n+1)×n×(n−1) +5!n(n+1)(n−1)(n−2) ] n+11[2n+1−1] n+12n Hence the option A is the correct answer.

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{C_0}{1} + {C_2}{3} + {C_4}{5} + {C_6}{7} ..... =

Question

$\frac{C _{0}}{1} + \frac{C _{2}}{3} + \frac{C _{4}}{5} + \frac{C _{6}}{7} ..... =$

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

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

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

None of these

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\frac{C _{0}}{1} + \frac{C _{2}}{3} + \frac{C _{4}}{5} + \frac{C _{6}}{7} ..... =

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Text solutionVerified

\frac{C _{o}}{1} + \frac{C _{2}}{3} + \frac{C _{4}}{5} + \frac{C _{6}}{7} ..... 1 + \frac{n \times ( n - 1 )}{3 !} + \frac{n \times ( n - 1 ) ( n - 2 ) ( n - 3 )}{5} + ...... \frac{1}{n + 1} [(n + 1) \frac{( n + 1 ) \times n \times ( n - 1 )}{3 !} + \frac{n ( n + 1 ) ( n - 1 ) ( n - 2 )}{5 !}] \frac{1}{n + 1} [2^{n + 1 - 1}] \frac{2 ^{n}}{n + 1}

Hence the option

A

is the correct answer.

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Question Text	$\frac{C _{0}}{1} + \frac{C _{2}}{3} + \frac{C _{4}}{5} + \frac{C _{6}}{7} ..... =$
Answer Type	Text solution:1
Upvotes	150

1C0​​+3C2​​+5C4​​+7C6​​.....=

Text solutionVerified

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$\frac{C _{0}}{1} + \frac{C _{2}}{3} + \frac{C _{4}}{5} + \frac{C _{6}}{7} ..... =$