Summing a function

Algebra Level 3

Let

f ( x ) = 2 4 x + 2 f (x) = \frac {2}{4^x + 2}

for all real numbers x x . Evaluate

f ( 1 2001 ) + f ( 2 2001 ) + f ( 3 2001 ) + . . . + f ( 2000 2001 ) f (\frac {1}{2001}) + f (\frac {2}{2001}) + f (\frac {3}{2001}) + ... +f (\frac {2000}{2001}) .


The answer is 1000.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Eddie The Head
Apr 16, 2014

Hint: \textbf{Hint:} We see that f ( x ) + f ( 1 − x ) = 1 f(x) + f(1-x) = 1

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Duplicate. Also this problem is from the book '101 Problems in Algebra'.

Jubayer Nirjhor - 6 years, 6 months ago

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