hi

Question

i startted the problem below by writing a sigma notation
of
sigma[(2^(n+1))/((n+1)!)]

QUESTION:

how do i find the sum of 2+(4/2!)+(8/3!)+(16/4!)+...

was my attempt wrong, or how do i go from here? thank you!

Answer 1

Express the individual elements of each term in terms of i.
For the 3rd term, i=3, then
8/3!=2*³/3! = 2³/i!
Verify with another term:
for i=4,
2^i/i!=16/4! = 4th term, OK
Check the first term (which does not have the same form), i=1
2^1/1! = 2/1 = 2 OK

So the sum would be:
Σ2^i /i! for i=1 to ∞