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1/(1(n-1)!)+1/(2!(n-)!) +1/(5!(n-5)!)+.....

`1/(1(n-1)!)+1/(2!(n-)!) +1/(5!(n-5)!)+...` is equal to

A

` (2^(n-4))/(n!)` for even values of n only

B

` (2^(n-4)+1)/(n!)-1` for odd values of n only

C

` (2^(n-1))/(n!)` for all values of n

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
c
Let ` S = 1/(n!) [ (n!)/(1!(n-1)!)+(n!)/(3!(n-3)!)+(n!)/(5!(n-5)!)+...]`
` = 1/(n!) [ .^(n)C_(1)+.^(n)C_(3)+.^(n)C_(5)+...] = 1/(n!) * 2^(n-1)` for all values of n
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SEQUENCES AND SERIES -EXERCISE 24
  1. 1/(1(n-1)!)+1/(2!(n-)!) +1/(5!(n-5)!)+... is equal to

    Text Solution

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