SOLUTION: An infinite geometric series has common ratio r. The sum to infinity of the series is four times the first term. Show that r = 0.75

Algebra ->  Sequences-and-series -> SOLUTION: An infinite geometric series has common ratio r. The sum to infinity of the series is four times the first term. Show that r = 0.75      Log On


   



Question 424600: An infinite geometric series has common ratio r. The sum to infinity of the series is four times the first term.
Show that r = 0.75

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can assume the first term is 1, and subsequent terms r, r%5E2, ... where -1+%3C=+r+%3C=+1. The sum is therefore 1%2F%281-r%29. If this is equal to four times the first term, then

1%2F%281-r%29+=+4

4%281-r%29+=+1

From this, we obtain r+=+0.75.