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GoGoDancer12
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Homework Statement
Prove that H1 +H2 +...+Hn = (n +1)(Hn-n)?
Homework Equations
Hn denotes the nth harmonic number.
The nth harmonic number is the sum of 1+1/2+...1/n,
which is n / n +1.
I'm not really sure if Hn = (1/ n) .
Prove by Mathematical Induction
Hn denotes the nth harmonic number.
The Attempt at a Solution
Basis Step : P(1) = Hn = (n +1)(Hn-n)
(1 / n) = (n +1) ( (1 / n) -n)
(1) = ( 1 + 1) (1-1)
1 = (2) (0)
1 = 0, which is false
or
Basis Step:
P(1) = Hn = Hn = (n +1)(Hn-n)
( n / n + 1) = (n + 1) ( (n / n + 1) -1)
P(1) is false, because 1/ 2 does not equal to - 1