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Question
If f(x)=16^x/ 16^x+4, find the value of f(1/852)+f(2/852)+f(3/852)+ ……..+f(851/852).
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Answer
f(x) = $$16^x/(16^x + 4)$$
f(1-x) = $$16^{1-x}/(16^{1-x}+4)$$ = $$16*16^x/[16^x*(16+4*16^x)]$$ = $$4/(16^x+4)$$
f(x) + f(1-x) = 1
f(1/852)+f(851/852) = 1
...
So, required sum = 1 + 1 + ... (425 times) + f(426/852) = 425 + f(1/2) = 425 + 0.5 = 425.5
