Please Help!!! Thanks!!!

M

math-a-phobic

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Feb 10, 2006
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Hi and thank you for youir time! I have just finished solving this word problem and received the formula 2^(x-1) and an amount of $92,233,720,368,547,758.08 . Could you please check to see if the formula and solution for this word problem is correct? Thank you! :D


Problem: You have just saved the king, and his kingdom, from a particularly strong and evil rival. In gratitude, the king offers you anything you desire. Since you are not only brave but also humble, you make the king this offer. He is to put one penny on the first square of a checkerboard, double it to two on the second square, and continue to double the amount of pennies on each successive square. And you will accpet the money on only the last square. How much does the king owe you?
 
Think about the last problem we done. This is even simpler. When you

double, what number do you think of?. How many squares on a

checkerboard?. Take that number to the power of the number of squares.

See what I mean?.
 
I think I see what you mean. The number I think of when I double is 2, and there are 64 squares on a checkerboard, so is the equation 2^64, but they only ask for the total on the 64th square, so wouldn't the function be 2^63 since you had 1 penny on the first square, 2 on the second, and 4 on the third? Making the formula for total on the 64th square only be
f(64)= 2^(64-1). Which one is do you think is correct? Thanks for the help! :D
 
Okay, I redid the problem over and should it look like this?
2(.5+1+2+4+8+16+32+64+128.......) all the way until you went up to the 63rd power right? Is there a simplier way?
 
Thanks Denis, I'm sorry for posting the same problem three times I didn't get a definite answer until now because I made so many mistakes in my posts. Thanks again, you were very helpful! :D
 
2^63 = 9223372036854775808

Don't forget tha you need to divide by 100, since we're using 2 instead of .02:
92233720368547758.08

So the formula really is: 2^(x-1) / 100
 
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