SOLUTION: Hi, having some problems with the following question any chance some one could step by step walk me though it please Q. find a formula for the sum of x^2+x^6+x^10+...+x^2+4

Algebra ->  Sequences-and-series -> SOLUTION: Hi, having some problems with the following question any chance some one could step by step walk me though it please Q. find a formula for the sum of x^2+x^6+x^10+...+x^2+4      Log On


   



Question 357898: Hi,
having some problems with the following question any chance some one could step by step walk me though it please
Q. find a formula for the sum of
x^2+x^6+x^10+...+x^2+4n+...+x^42
What will be the sum of the series when x = 1?
Also finding this one tricky to:
Q. obtain the sum of the infinite geometric progression
2-2/3+2/9-2/27+...
Any help would be very helpful
Thanks :)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
T=sum%28x%5E%282%2B4i%29%2Ci=0%2CN%29
Find the number of terms.
2%2B4N=42
4N=40
N=10
Since the terms start at 0 and not 1, then there are 11 terms altogether.
Eleven terms, each having a value of 1.
S=11%281%29
highlight%28S=11%29
.
.
.
S=2%2B2%2Asum%28%28-1%2F3%29%5En%2Cn=1%2Cinfinity%29
S=2%2B2%2A%28-%28%281%2F3%29%2F%281%2B1%2F3%29%29%29
S=2%2B2%2A%28-%28%281%2F3%29%2F%284%2F3%29%29%29
S=2-2%2A%281%2F4%29
S=2-1%2F2
highlight%28S=3%2F2%29