Patterns give rise to problems

Algebra Level 4

n = 1 100 1 0 n { 2 n + 2 n } \large\sum_{n=1}^{100} 10^n\{2^n+2^{-n}\}

If the above summation can be evaluated to be a b a c \dfrac{a^b-a}{c} where a , b a,b and c c are positive integers and a , c a,c are coprime, find the value of a + b + c a+b+c .

Notation : { } \{ \cdot \} denotes the fractional part function .


The answer is 110.

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1 solution

Abhisek Mohanty
Apr 9, 2016

Moderator note:

Simple standard approach.

Note that instead of taking a screenshot, you should simply copy-paste the Latex code. This allows you to easily edit the solution if necessary.

Calvin Lin Staff - 5 years, 2 months ago

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