A question from mah textbook... (geometric series)

[wakemeup]

Show that the sum to infinity of the geometric series 3+ 9/4 + 27/16 +.... and 4 + 8/3 + 16/9 +.... are equal.

[7ooD]

The sum to infinity of geometric series is A/1-r

Where A is the first term in the sequence

And R is the common ratio and R should be less than 1 and greater than -1

so in the sequence of 3+ 9/4 + 27/16 +....

A=3
R=0.75

Use the formula A/1-r

3/1-0/75 = 12

Second sequence 4 + 8/3 + 16/9 +....
A=4
R=2/3

4/1-(2/3) = 12

There they are equal