If f(x)=4^x/(4^x+2) , then f(1/97)+f(2/97)+f(3/97)+.........+f(96/97) is equal to (a)1 (b)48 (c)-48 (d)-1.

Explain pls.

Hi Aditi,

For the function mentioned,

Note that f(x) + f(1-x) = 4^x/(4^x+2) + 4^1-x/(4^1-x+2) = 4^x/(4^x+2) +2/(4^x+2) = 1

So f(1/97)+f(96/97) = f(1/97) + f(1-1/97) = 1

Similarly f(2/97)+f(95/97) = 1

So the required sum = 1+1+1+......48 times

Henct the required sum = 48.

Option (B)

Hope that helps.

Best Regards,

Ashwin (IIT Madras).