Question

`((1)/(2!)+(1)/(4!)+(1)/(6!)+…equals)/(1)+(1)/(3!)+(1)/(5!)+…`
A. e+1
B. `(e-1)/(e+1)`
C. e-1
D. none of these

Answer 1

Answer:
We have
`(e+e^(-1))/(2)=1+(1)/(2!)+(1)/(4!)+(1)/(6!)`……
and `(e-e^(-1))/(2)=(1)/(1!)+(1)/(3!)+(1)/(5!)+(1)/(7!)`+….
`therefore ((1)/(2!)+(1)/(4!)+(1)/(6!))/(1+(1)/(3!)+(1)/(5!))+…..=(e+e^(-01))/(2)-(1)/(e-e^(-1)/(2))=((e-1)^(2))/(e^(2)-1)=(e-1)/(e+1)`