SOLUTION: Find the sum of the infinite series (if it exists) <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/7-1.png" alt="Photobucket

SOLUTION: Find the sum of the infinite series (if it exists) <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/7-1.png" alt="Photobucket - Video and Image Hosting">

Question 172793: Find the sum of the infinite series (if it exists)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Take note that the terms form a geometric sequence (since there is a common ratio and exponent involved)

Recall, the formula for a geometric sequence is where

Since the coefficient is 300, this tells us that

Since the value being raised to a power is , this means that

So the formula is . So, for instance, if , then (which is the third term).

Also, remember that the formula for an infinite geometric series is

Since we're starting at n=1, the series needs to be rewritten to

So in this case, the formula we'll use is

So the sum of the infinite series is
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