Find the sum of the infinite series: 1/2 + 1/6 + 1/12 + 1/20 + ...
Correct: E
The series can be written as 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... This is a telescoping series. 1/(n(n+1)) = 1/n - 1/(n+1). The sum is (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... The partial sum is 1 - 1/(n+1). As n approaches infinity, 1/(n+1) approaches 0, so the sum of the series is 1.