Question

How do you do this question?

Answer 1

Answer:   25/12

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Work Shown:

$\displaystyle S_n = \sum_{k=1}^{n} \frac{1}{k}\\\\\\\displaystyle S_4 = \sum_{k=1}^{4} \frac{1}{k}\\\\\\\displaystyle S_4 = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\\\\\\\displaystyle S_4 = \frac{12}{12}+\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\\\\\\\displaystyle S_4 = \frac{12+6+4+3}{12}\\\\\\\displaystyle S_4 = \frac{25}{12}$

Note: in step 3, I'm adding terms in the form 1/k where k ranges from k = 1 to k = 4 (k being an integer)