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What is the nth term of the series 4, 44, 444, 4444,…  

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xetaalpha2 | Student | (Level 2) Honors

Posted April 18, 2011 at 2:20 PM via web

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What is the nth term of the series 4, 44, 444, 4444,…

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 18, 2011 at 2:35 PM (Answer #1)

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The series given is 4 , 44 , 444 , 4444 ,…

This series is none of the general ones that we encounter like arithmetic series, geometric series or harmonic series.

To find the nth term look at each term. The 1st can be written as 9*(4/9), the next 99*(4/9), followed by 999*(4/9), 9999*(4/9),...

9 , 99, 999, 9999 can be written as 10 – 1 , 100 – 1 , 1000 – 1 and 10000 – 1

or generally as 10^n – 1

The nth term of the given series is (4/9)*[10^n – 1]

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