I have a box with 64 blocks in, a chess field, I'm playing against a opponent and we decide to put 1 cent in the first field, and 2 cent in the second and double the previous amount every time for all 64 blocks. is my response of (2^64 - 1) correct to the total sum of money we would have to give the winner?

Question

anonymous · Answer

No! thats just the amount in the last square.  You have to add all the squares together to get the number total. $$\sum_{n=0}^{63}2^n$$

anonymous · Answer

okay... so I the formula?

anonymous · Answer

It is equal to 18446744073709551615 cents.

anonymous · Answer

wooooww okay, but why put 63 and not 64 by the sum?

anonymous · Answer

Because we are starting counting at 0 instead of 1 like we normally would if we were speaking.  IE. There are 64 numbers between 0 and 63

anonymous · Answer

One for each space on the board.

anonymous · Answer

ahhh okay

anonymous · Answer

Yeah, it confuses me all the time.  It usually helps to wright out the first few numbers in the sequence.

anonymous · Answer

okay hehe yeah that confused me totally

anonymous · Answer

You could also wright it as 1(for the first square) + $$\sum_{n=1}^{63}2^n$$

anonymous · Answer

okay, but how would I write out this equation if I were to need to do it in a exam?
I took this out of a practice test:

Marie and Thandi play chess. They decided that the loser one cent in the first square of the chessboard will
instead, two cents in the second square, four cents in the third box - thus doubling the amount in each box
for all 64 blocks.

a.) After the amount of money that the winner would receive, calculated, they realize that none of
them much money. Do a calculation to determine whether their response to (2 ^ 64-1) is correct.

b.) Marie suggests that they amount to the tenth box as prize money. Calculate the amount of money

anonymous · Answer

how should I go about writing it for maximum marks? I wasn't in class so I'm trying to self study it

anonymous · Answer

If you wrote basically what i said about only counting the values of the last cell, and showed the summation formula i gave you, you should get full credit.  As for part b you would only go to 9 in the sum.

anonymous · Answer

okay, seems to easy... I always feel its to simple.

anonymous · Answer

summination formula is which one again? sorry I'm not english and I don't do maths in english I try to learn it in english now hehe

anonymous · Answer

is it the Sn = a/2 [a + (n-1)d] ?