Question
Find the sum of the series
2 + 9/2! + 27/3! + 81/4! . . .
2 + 9/2! + 27/3! + 81/4! . . .
Answers
Count blis
2 + 9/2! + 27/3! + 81/4! + ...
Sum from k = 0 to infinity of 3^k/k! -2
= exp(3) - 2
Sum from k = 0 to infinity of 3^k/k! -2
= exp(3) - 2
Damon
-1 + ( 3 + 3^2/2! + 3^3/3! + 3^4/4! ..)
but e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! ....
so
e^3 - 1 = 3 + 3^2/2! + 3^3/3! + 3^4/4! ....
so we have
-1 + e^3 -1 = -2 + e^3
but e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! ....
so
e^3 - 1 = 3 + 3^2/2! + 3^3/3! + 3^4/4! ....
so we have
-1 + e^3 -1 = -2 + e^3
julia
i don't understand the last step. how did you get to -1 + e^3 -1 = -2 + e^3