First time poster, forgive me in advance.
I am trying to get a function out of the following series that goes on for infinity. I'm pretty sure this is possible as I was able to solve the problem using Excel but I'm stumped when trying to assign a function to it that can be done by hand.
The series is:
1.1/1.12 + 1.2/1.12^2 + 1.3/1.12^3 + 1.4/1.12^4 + ... to infinity
When I solve this in Excel I can get a value of 16.11 however I can't seem to get this number by hand. Is it possible to do by hand, and if so, how?
Please let me know if I need to clarify anything.
Thank you in advance.
Hello, ShoelessJoe!
Welcome aboard!
Evaluate: .
We are given the series: .
Multiply by
Subtract: . . . .
And we have: . . . . .
The geometric series has first term and common ratio
. . Its sum is: .
Then we have: .
Therefore: .
Please check for egregious blunders . . .
.