Question 53425
See if this makes sense to you! If you double the number of pennies on each succeeding square, starting with one penny, the progression would look like this:
Square...1...2...3...4...5...6...   ...n
Pennies..1...2...4...8...16..32..  ..{{{2^(n-1)}}}
a) So then, on the 32nd square, n = 32 and the number of pennies would be: {{{2^(32-1) = 2^31}}} = 2,147,483,648 pennies = $21,474,836.48

Answer a) is: $21,474,836.48

b) The total number of pennies required to fill a 32-square checker board would be:
1+2+4+8+16+...+{{{2^(31)}}} = {{{2^32 - 1 = 4294967296 - 1}}} = 4,294,967,295 pennies = $42,949,672.95

c) The total number of pennies required to fill a 64-square checker board would be:
{{{2^64 - 1}}} = 18,446,744,073,709,551,615 pennies = $184,467,440,737,095,516.15