Please help me, I don't understand how they got this answer?

Notice the numerators -- they are 2, 4, 6, 8, i.e., the even integers. And the denominators -- 1, 3, 5, 7, i.e., the odd integers. You would reason that these patterns would continue: next values would be 10/9, 12/11, 14/13. Now it's a matter of expressing these as general terms. Even numbers are 2n, where n = 1, 2, 3, etc. Odd terms are 2n -1, again with n = 1, 2, 3,... since we need 1 as the first value. This implies 2n/(2n-1)