SOLUTION: Find the sum of the geometric series: 1+ sqrt6+ 6+...+7776

Question 540972: Find the sum of the geometric series:
1+ sqrt6+ 6+...+7776
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Each term in the series is the previous one multiplied by .
It is a geometric series.

I multiplied by to rationalize (get rid of the square root in the denominator).
You may get to
from a carefully applied formula from your book, or (if allowed) deduce it from
sum*1=1+sqrt6+6+.....+7776, so
sum*sqrt6=sqrt6+6+6sqrt6+.....+7776*sqrt6, so subtracting
sum*sqrt6 - sum*1 = sum*(sqrt6-1)=7776*sqrt6-1
ALTERNATE WORK-UP
We knew it had to be a power of 6.
can be grouped as

and the parentheses can be easily calculated as
and

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