Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Fraction Addition with Arithmetic Series as Denominators

Does anyone know how to add these fractions?

Like my previous question, I believe this one also has something which can be canceled out, and the denominators contain arithmetic series. Can this series be used to make some sorts of shortcuts?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: [ASK] Fraction Addition with Arithmetic Series as Denominators

It can be proven that the sum of an arithmetic series with general difference of 1 is given by:

hence the given series can be written as:

The last expression is deduced like the previous question.