SOLUTION: the sum of the first n terms of a series is 2n^-n find the nth term

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Question 1050630: the sum of the first n terms of a series is 2n^-n find the nth term
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

What do you mean by 2n^-n with only a caret ^ to indicate 
an exponent but then there is no exponent after it?

Maybe you meant 2n%5E2-n and should have written 2n^2-n. 
Is that it?  I'll guess that's what you meant.

The first term has to be just the "sum of the first term
only", [even though nothing has been summed!] but that's
how we consider "summing" when there is only one number.
So the first term has to be 2(1)^2-1 or 2(1)-1 = 2-1 = 1.
a1 = 1.  Then for n > 1



The sum of the first n terms = 2n%5E2-n
The sum of the first n-1 terms = 2%28n-1%29%5E2-%28n-1%29

So, nth term = %282n%5E2-n%29-%282%28n-1%29%5E2-%28n-1%29%5E%22%22%29%22%22=%22%22 
               
               2n%5E2-n-%282%28n%5E2-2n%2B1%29%5E%22%22-n%2B1%29%29%22%22=%22%22  

               2n%5E2-n-%282n%5E2-4n%2B2-n%2B1%29%29%22%22=%22%22

               2n%5E2-n-%282n%5E2-5n%2B3%29%29%22%22=%22%22

               2n%5E2-n-2n%5E2%2B5n-3%29%22%22=%22%22

               4n-3%29

Edwin