Trivial Summation Challenge Write the repeating decimal 1.367367367367... in the form a / b where both a an b are positive whole numbers, but do this using a converging infinite sum.

Question

Trivial Summation Challenge Write the repeating decimal   1.367367367367... in the form   a      /    b where both   a an   b are positive whole numbers, but do this using a converging infinite sum.

Donavan Mack · Accepted Answer

Rewrite your numer as  1  +  0.367367  …and notice that the latter term can be rewritten as      ∑          n      ≥      1            367          10              3        n              .Now notice that this is nothing but an infinite geometric series. Conclude.

varitero5w · Accepted Answer

And, ignoring the requirement for an infinite sum, if   x  =  1.367367367367..., then   1000  x  =  1367.367367367... so   999  x  =  1366 so   x  =            1366      999

Trivial Summation Challenge Write the repeating decimal 1.367367367367...

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