September 13th, 2017, 04:09 PM  #1 
Newbie Joined: Jan 2017 From: USA Posts: 11 Thanks: 0  Geometric Series Question.
Why is the formula for a geometric series (n+1)a, where the initial term is a, whenever the common ratio is 1? I would have expected it to be a(n) because the upper limit of the summation is n. So it would be a + a + a +... + a, n times. Not n+1 times. Why is it n+1? 
September 13th, 2017, 06:06 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,728 Thanks: 689 
It depends on the lower limit. For 0, you get n+1. For 1, you get n. I presume 0 was intended.

September 13th, 2017, 07:44 PM  #3 
Newbie Joined: Jan 2017 From: USA Posts: 11 Thanks: 0  
September 14th, 2017, 04:11 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
The "geometric series", by convention, starts with "i= 0", not 1. $\displaystyle \sum_{i= 0}^n ar^i= a+ ar+ ar^2+ \cdot\cdot\cdot+ ar^n$ counting the "i=0" term there are n+1 terms in the sum so if r= 1 that is a(n+1). Last edited by skipjack; September 14th, 2017 at 04:18 AM. 

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