What is the value of the sum of the infinite series 1 + 1/2 + 1/3 + 1/4 + ...?
Correct: D
The series 1 + 1/2 + 1/3 + 1/4 + ... is known as the harmonic series. The harmonic series is a divergent series, meaning that its sum approaches infinity as the number of terms increases without bound. This can be proven by grouping the terms of the series as follows: 1 + 1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) + ... . Each group of terms in parentheses has a sum greater than 1/2, so the total sum of the series is greater than 1 + 1/2 + 1/2 + 1/2 + ... . Since this sum approaches infinity, the harmonic series diverges.