** Claim: **

*Proof. * The proof is by induction. If then on the left we have

On the right,

So, indeed, the formula holds for the case .

Assume then that the formula is true for some . Then,

Thus, the formula holds for ; and thus, for all

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#
Stumbling Robot

A Fraction of a Dot
#
Find a formula for a sum of 1/k(k+1)

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2 comments

### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

** Claim: **

*Proof. * The proof is by induction. If then on the left we have

On the right,

So, indeed, the formula holds for the case .

Assume then that the formula is true for some . Then,

Thus, the formula holds for ; and thus, for all

You can also do this with a telescoping sum, since k/(k+1) – (k-1)/k = 1/(k(k+1)).

Buenos dias, quisiera saber porque al hacer la suma de fraccionarios, da n+2-1 y no n+2+1, ya que es una suma de fraccionarios y no una resta, gracias.