math

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hi
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!

  • math -

    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 ∞

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