+44 On a calendar, I put 1 grain of sand on May 1st, 2 grains of sand on May 2nd, 4 grains on May 3rd, and so forth, doubling the number of grains each day. On what day will I put down the 500th grain?
+129852 We can use the sum of a geometric series to solve this
Sum = First term [ 1 - (common ratio)^n ] / [ 1 - common ratio]
The common ratio is 2....and we are trying to find " n".....so we have
500 = 1 [ 1 - 2^n ] / [1 - 2 ]
500 = 1 [ 1 - 2^n ] / [ - 1 ] multiply both sides by -1
- 500 = 1 - 2^n subtract 1 from both sides
-500 - 1 = -2^n
-501 = - 2^n multiply both sides by -1
2^n = 501 take the log of both sides
log 2^n = log 501 and we can write
n * log (2) = log (501) divide both sides by log (2)
n = log (501) / log (2) ≈ 8.96 days
