Proving the Harmonic Series Sum Formula for Positive Integers | Math Proof

[James889]

Hai,

The harmonic series is given by: H_{n} = \sum_{i=1}^n \frac{1}{i}

I need to prove that for all positive integers:
\sum_{j=1}^n H_{j} = (n+1)H_{n} -n

So i have
H_{5} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{137}{60}

H_{5} \neq (5+1)*\frac{137}{60} -5

Have i missed something here?

Please excuse my epic fail math skills...

 

[Office_Shredder]

So for your H₅ example what they want you to sum is

H₁ + H₂ + H₃ + H₄ + H₅

When I did that I got what the problem tells you you will get