SOLUTION: Find the sum of the series 1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100).

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum of the series 1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100).      Log On


   

Question 1133988: Find the sum of the series 1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The sum

1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100)

is equal to

1/2+2/2+3/2+...+99/2

This is an arithmetic series with 99 terms; the sum is 99 times the average of the first and last:

99%28%281%2F2%2B99%2F2%29%2F2%29+=+99%2A25+=+2475