The sum of the series
`(1)/(1!19!)+(1)/(3!17!) +(1)/(5!15!) + .........` to 10 terms is equal to

Options

A. `((2^(19)-1))/(20!)`
B. `(2^(20))/(20!)`
C. `(2^(10))/(20!)`
D. `(2^(19))/(19!)`

Answer

a

Explanation

We have,
`S = (1)/(19!) + (1)/(3!17!)+(1)/(5!15!)+.........` to 10 terms
`rArr S = (1)/(20!) { (20)/(1!19!)+(20)/(3!17)+(20!)/(5!15!)+........."to 10 terms"}`
`rArr S = (1)/(20!) {""^(20)C_(1)+ ""^(20)C_(3)+""^(20)C_(5)+........+""^(20)C_(19)+}`
`rArr S = (1)/(20!) {2^(20-1)}= (2^(19))/(20!)`.