Question

If `x-x^2/2+x^3/3+x^4/4+.....` to `oo=y` , then `y+y^2/(2!)+y^3/(3!)+....` + to `oo` is equal to
A. `e^(y)-1`
B. `log_(e)(1+y)`
C. `x^(3)=e^(y)`
D. `x=1+e^(y)`

Answer 1

Answer:
We have
`y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)`+..
`rarr y= log_(e)(1+x)rarre^(y)=1+xrarrx=e^(y)-1`