If P is a projection matrix, show from the initial series that e^P=I+1.718P

I know P^k=P, but I'm not sure what "from initial series" means. Thank you!

e^x = 1+ x+ x^2/2! + x^3/3! + ....
plug x=1--> e = 1+1+1/2! + 1/3! +....
and
e^A = I + A + 1/2! (A^2) + 1/3! (A^3) + .....
Plug A= P
e^P = I + P + 1/2! (P^2) + 1/3! (P^3) + .....

Since P^k = P
e^P= I + P + 1/2! (P) + 1/3! (P) + .....
= I + P(1+1/2! + 1/3! + ....)
= I + P(e -1)
= I + (1.718....)P