Question

The sum of the series `1+1/4.2!1/16.4!+1/64.6!+………to oo` is (A) `(e+1)/2sqrt(e)` (B) `(e-1)/sqrt(e)` (C) `(e-1)/+2sqrt(e)` (D) `(e-1)/sqrt(e)`
A. `(e+1)/(2sqrt(e )`
B. `(e-1)/(2sqrt(e )`
C. `(e+1)/(2sqrt(e )`
D. `(e-1)/(2sqrt(e )`

Answer 1

Answer:
we have
`1+(1)/(4.2!)+(1)/(16.4!)+(1)/(64.6!)…to infty`
=`1+(1)/(2!)(1/2)^(2)+(1)/(4!)(1/2)^(4)+(1)/(6!)(1/2)^(6)+… to infty`
`=(e^(1//2)+e^(-1//2))/(2)`
before `[(e^(x)+e^(-x))/(2)=1+(x^(2))/(2!)+(x^(4))/(4!)+(x^(6))/(6!)+…]`
`=(e+1)/2sqrt(e )`