Suppose $f(x)=\frac{4^x}{4^x+2}$ and prove that $f\left(\frac{1}{1997}\right)+f\left(\frac{2}{1997}\right)+\ldots+f\left(\frac{1996}{1997}\right)=998$

Asked Feb 19 '21 at 19:08

Active Feb 19 '21 at 19:13

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Suppose $f(x)=\dfrac{4^x}{4^x+2}$ and prove that $$f\left(\dfrac{1}{1997}\right)+f\left(\dfrac{2}{1997}\right)+\ldots+f\left(\dfrac{1996}{1997}\right)=998.$$

I tried to do the problem but I could not get started. Substituting the value of $x$ seems to be too lengthy.

edited Feb 19 '21 at 19:13

Angelo

12,328

asked Feb 19 '21 at 19:08

Principia Mathematica

Sum the first and last term. You will see an order. – beingmathematician Feb 19 '21 at 19:10
1

https://math.stackexchange.com/q/3500411/42969, https://math.stackexchange.com/q/2401137/42969 – Martin R Feb 19 '21 at 19:11

Suppose $f(x)=\frac{4^x}{4^x+2}$ and prove that $f\left(\frac{1}{1997}\right)+f\left(\frac{2}{1997}\right)+\ldots+f\left(\frac{1996}{1997}\right)=998$

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