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Arthimetic and Geometric

dwsmith

Well-known member
Feb 1, 2012
1,673
Is it true that geometric progressions are \leq arithmetic?
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Doesn't seem a far shot. We know that arithmetic mean is greater or equal than geometric mean, perhaps applying that you could get to your result. Are we assuming finiteness or not?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621

dwsmith

Well-known member
Feb 1, 2012
1,673
I am wondering if GP $\leq$ AP
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
I am wondering if GP $\leq$ AP
So your question seems to be whether the sum of any arithmetic progression is greater than or equal to the sum of any geometric progression. That is not the case. For example, \(1,\,3,\,5\) is an arithmetic progression and \(2,\,4,\,8\) is a geometric progression. But, \(1+3+5=9\mbox{ and }2+4+8=14\)
 
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