SOLUTION: write in summation notation: 3/5 + 3/4 + 15/16 + 75/64 + .......

Algebra ->  Finance -> SOLUTION: write in summation notation: 3/5 + 3/4 + 15/16 + 75/64 + .......      Log On


   

Question 1029340: write in summation notation:
3/5 + 3/4 + 15/16 + 75/64 + .......
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Checking to see if it is a geometric sequence:







So it is a geometric sequence with a%5B1%5D=3%2F5 and r=5%2F4

The kth term is a%5Bk%5D=ar%5E%28k-1%29=expr%283%2F5%29expr%28%285%2F4%29%29%5E%28k-1%29

In summation notation for the first n terms:



We may factor out the 3%2F5



Note: Your teacher may have wanted you to sum to infinity, instead
of only to n.  The reason I did not is because the series diverges 
since r > 1.

Edwin