please show the works and indicate which option is the right answer . thanks

Find a power series representation for the function O 1 . f (y ) = (-1)n 2n+lyn 1 n=0 f(y ) = 2ty O 2. f(y) = 1 2n+1 ?" n=0 O 00 3. f(y) = (-1)"2y" n=0 4. f(y) = E (-1)ngn+1 yn n=0 O 5. f(y) = 2ntlyn n=0