Question 84069
Your first answer is correct:
The number of pennies on the 32nd square would be:
{{{2^(32-1) = 2^31}}} = 2147483648 and this would be: $21,474,836.48 which is exactly what you have!
Your second answer is correct.
The total amount on a 32-square checkerboard would come to:
{{{2^32 - 1 = 4294967295}}}pennies and this would be: $42,949,672.95
Your third answer seems to be off by a penny:
The total amount on a 64-square checkerboard would be:
{{{2^64 - 1 = 18446744073709551616-1}}}pennies and this would be: $184,467,440,737,095,516.15