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March 6, 2015

Posted by **Anonymous** on Sunday, September 18, 2011 at 8:06pm.

What would be an expression for the total amount of grain needed to fulfill Anna's request.

- Calculus -
**Reiny**, Sunday, September 18, 2011 at 8:40pmclearly

1+2+4+8+ ... + for 64 terms

a GS, where a=1, r=2 and n=64

sum(64) = 1(2^64 - 1)/(2-1)

= 2^64 - 1

notice for this series

sum(2) = 3 = 2^2 - 1

sum(3) = 7 = 2^3 - 1

sum(4) = 15 = 2^4 - 1

...

sum(64) = 2^64 - 1

- Calculus -
**Damon**, Sunday, September 18, 2011 at 8:43pm2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

say you had three squares. labeled 1, 2 and 3

the first square has 2^0 = 1

the second square has 2^1 = 2

the third square has 2^2 = 4

now go on to 64 th square has 2^63

now 2^63 = approximately 9.33 * 10^18

- Oh, sorry -
**Damon**, Sunday, September 18, 2011 at 8:45pmI gave you the amount on the last square. Use Reiny's system.

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