Posted by Olivia on Sunday, March 10, 2013 at 1:46pm.
2+4+8+...is a geometric sequence. Prove the sum of the first n terms is two less than the (n+1)the term.

Mathematics. Geometric sequences.  Reiny, Sunday, March 10, 2013 at 3:25pm
a = 2 , r = 2
sum(n) = 2(2^n  1)/(21) = 2(2^n  1)
= 2^(n+1)  2
sum(n+1) = 2(2^(n+1)  1)/1 = 2(2^(n+1)  1)
= 2^(n+2)  2
sum(N+1)  sum(n) =2^(n+2)  2  (2^(n+1)  2)
= 2^(n+2)  2^(n+1)
= 2^(n+1) (2  1)
= 2^(n+1) , which is a positive number
so sum(n) < sum(n+1)
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