My Math Forum Geometric Series Question.

 Calculus Calculus Math Forum

 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: 6,807 Thanks: 717 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

Quote:
 Originally Posted by mathman It depends on the lower limit. For 0, you get n+1. For 1, you get n. I presume 0 was intended.
Wait, I think I see it. The summation is on ar^j, for j = 0,1,2,...,n

If r is 1, then we add a to itself n times, plus a zeroth time. Right? So it's n+1, and not n.

 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.

 Tags geometric, question, series

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Fozmass Applied Math 2 August 7th, 2014 05:23 AM Fozmass Applied Math 3 August 3rd, 2014 04:04 PM Math_slayer Algebra 5 May 11th, 2012 07:30 PM The_big_dill Algebra 5 June 1st, 2010 05:16 AM Math_slayer Real Analysis 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top