Function Frenzy

Level 2

Let f ( x ) = 2 2 x 2 2 x + 2 f(x)=\frac{2^{2x}}{2^{2x}+2} for every x ∈ R x \in \mathbb{R} . What is the value of ⌊ ∑ n = 1 2013 f ( n 2014 ) ⌋ \left \lfloor \sum_{n=1}^{2013}f\left(\frac{n}{2014}\right) \right \rfloor ?


The answer is 1006.

Hahn Lheem by Hahn Lheem , 21, USA

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2 solutions

Shinjita Awasthi
Jul 1, 2020

Using the reflection formula, n—> 2014-n And then, S(sum) = 0.5 * ( S + S ) Gives S= 1006.5 Now, after rounding off, Ans: 1006

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Ayush Sharma
Jul 11, 2015

The actual answer is 1006.5 but rounding it off gives the answer as 1006

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