imc

Question

Consider the set of numbers 1, 10, 10^2, 10^3, , 10^10. The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?

Accepted Answer

The requested ratio is 10^1010^9 + 10^8 + + 10 + 1. Using the formula for a geometric series, we have 10^9 + 10^8 + + 10 + 1 = 10^10 - 110 - 1 = 10^10 - 19, which is very close to 10^109, so the ratio is very close to 9.