Answer:
Square 15: 16,384
Sum of all grains up to and including square 15: 32,767
Total weight up to and including square 15: 4.681 lb
Step-by-step explanation:
Square 1: 1 = 2^0
Square 2: 2 = 2^1
Square 3: 4 = 2^2
Square 4: 8 = 2^3
Notice that the exponent of the 2 is 1 less than the number of the square, so for square n, the number of grains is 2^(n - 1)
Square n: 2^(n - 1)
Square 15: 2^(15 - 1) = 2^14 = 16,384
Now let's look at the sums.
Square 1 sum: 1
Square 2 sum: 1 + 2 = 3
Square 3 sum: 3 + 4 = 7
Square 4 sum: 7 + 8 = 15
Notice that each sum is one grain less than 2 raised to the number of the square.
Square 1 sum: 1 = 2^1 - 1
Square 2 sum: 1 + 2 = 3 = 2^2 - 1
Square 3 sum: 3 + 4 = 7 = 2^3 - 1
Square 4 sum: 7 + 8 = 15 = 2^4 - 1
Square n sum: 2^n - 1
Square 15 sum: 2^15 - 1 = 32,767
Weight:
32,767 × 1/7000 lb = 4.681 lb
