SOLUTION: The sum of the series 1/√3+1+3/√3+........... To 18 terms is ??

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Question 1113759: The sum of the series 1/√3+1+3/√3+........... To 18 terms is ??
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It is a geometric series, with first term b=1%2Fsqrt%283%29 and common ratio r=sqrt%283%29 .
The sum of the first n terms of a geometric series with first term b and common ratio r is
b%28%28r%5En-1%29%2F%28r-1%29%29 .

In this case, the sum of the first n=18 terms would be
%281%2Fsqrt%283%29%29%28%28sqrt%283%29%5E18-1%29%2F%28sqrt%283%29-1%29%29%22=%22%281%2Fsqrt%283%29%29%28%28%283%5E%221+%2F+2%22%29%5E18-1%29%2F%28sqrt%283%29-1%29%29%22=%22%22=%22%22=%2219682%283%2Bsqrt%283%29%29%2F%283%283-1%29%29%22=%2219682%283%2Bsqrt%283%29%29%2F6%22=%22highlight%289841%283%2Bsqrt%283%29%29%2F3%29%22=%22approximately15522.7

ANOTHER WAY:
The 9 even numbered terms are
matrix%281%2C7%2C%0D%0A1%2C%22%2C%22%2C3%2C%22%2C%22%2C9%2C%22%2C...%2C%22%2C3%5E8=6561%29 and add up to 1%283%5E9-1%29%2F%283-1%29=%2819683-1%29%2F2=9841 .
The 9 odd numbered terms must add up to 9841%2Fsqrt%283%29 .
Adding up both of those sums, we get