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)/(2-1) = 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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