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) (1)/(k)\\\\\\\displaystyle S_4 = \sum_(k=1)^(4) (1)/(k)\\\\\\\displaystyle S_4 = (1)/(1)+(1)/(2)+(1)/(3)+(1)/(4)\\\\\\\displaystyle S_4 = (12)/(12)+(6)/(12)+(4)/(12)+(3)/(12)\\\\\\\displaystyle S_4 = (12+6+4+3)/(12)\\\\\\\displaystyle S_4 = (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)