Let
P = 1/7 + 1/7^2 + 1/7^3 + ...
Then P can be expressed in the form a/b, where a and b are positive integers. Find the smallest possible value of a + b?
You have listed 3 terms for P. But 2 terms only give you the smallest a and b:
P ==1/7 + 1/7^2 ==a/b ==8 / 49. So: a + b ==8 + 49 ==57
If have to evalute 3 terms, as you have it listed, you get: a==57 and b==343
P is the sum of an infinite geometric series with initial term = 1/7 and ratio 1/7.
Using the formula for the sum: sum = (1/7) / ( 1 - 1/7 ), you can get the sum and the answer to the question.
