perplexus.info :: Just Math : Fractional Sum Quickie

Fractional Sum Quickie (Posted on 2023-07-31)

Using only p&p and a hand-calculator, determine the value of this expression:

    1    1      1        
1 + - + --- + ----- + ...
    3   3x6   3x6x9

See The Solution Submitted by K Sengupta

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Solution

Comment 1 of 1

Rewrite each term as a quotient of power of 1/3 and a factorial:

(1/3)^0/0! + (1/3)^1/1! + (1/3)^2/2! + (1/3)^3/3! + ...

Then this is simply the series expansion of e^x evaluated at 1/3.

Then the infinite sum evaluates to e^(1/3), and any scientific calculator can easily compute the numeric value as 1.395612425...

Posted by Brian Smith on 2023-07-31 10:42:54

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