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if f:R to R is given by f(x) = 9^x/9^x +3
for all x belongs to R
then f(1/1996) +f(2/1996)+......f(1995/1996)
997.5
998
997
998.5
Original post by Joel Raj
if f:R to R is given by f(x) = 9^x/9^x +3
for all x belongs to R
then f(1/1996) +f(2/1996)+......f(1995/1996)
997.5
998
997
998.5


You can prove algebraically that f(x) + f(1-x) is equal to 1 for all x. Now pair up the terms in your sum to make use of this. See https://www.quora.com/If-f-x-frac-9-x-3+9-x-how-do-we-find-f-frac-1-1996-+f-frac-2-1996-+-cdots-+f-frac-1995-1996 if you get stuck.

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