SOLUTION: 1+2+4+8+16+32+...+65,536 Find the sum of each sequence of numbers. Help?

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Question 843411: 1+2+4+8+16+32+...+65,536 Find the sum of each sequence of numbers. Help?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That is a geometric series,
the sum of the first 17 terms of the form
b%5Bn%5D=2%5E%28n-1%29 ,
because 2%5E16=2%5E4%2A2%5E10=64%2A1024=65536 .
That sum is SUM=1%2B2%2B2%5E2%2B2%5E3%2B%22...%22%2B2%5E16 and
2%2ASUM=2%2B2%5E2%2B2%5E3%2B%22...%22%2B2%5E16%2B2%5E17 , so
2%2ASUM-SUM=2%5E17-1
%282-1%29%2ASUM=131072-1
SUM=highlight%28131071%29

NOTE:
Your teacher/instructor may insist on seeing formulas, such as
sum%28b%5B0%5D%2Ar%5E%28n-1%29%2C+1%2Cn%29=b%5B0%5D%2A%28r%5En-1%29%2F%28r-1%29 , or SUM%5Bn%5D=b%5B0%5D%2A%28r%5En-1%29%2F%28r-1%29 .
Humoring teachers and bosses may be essential to survival,
but I do not believe math is about memorizing.
Remembering ideas that led others to a way to calculate results is OK.
That way we do not have to rediscover gunpowder every time,
but I refuse to memorize.