Let $f(x)=\frac{2^{x+2}+16}{2^{2x+1}+2^{x+4}+32}$. Then the value of $8\left(f\left(\frac1{15}\right)+f\left(\frac2{15}\right)+\dots+f\left(\frac{59}{15}\right)\right)$ is equal to

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] With $t=2^x$: $f(x)=\frac{4(t+4)}{2(t+4)^2}=\frac2{t+4}$. Then $f(x)+f(4-x)=\frac2{t+4}+\frac{2t}{4t+16}=\frac12$. Pair the terms $k$ and $60-k$ (29 pairs) giving $29\cdot\frac12$, and the middle term $f(2)=\frac14$. Sum $=14.75$; $8	imes14.75=118$. Answer (2).

Q. Let $f(x)=\frac{2^{x+2}+16}{2^{2x+1}+2^{x+4}+32}$. Then the value of $8\left(f\left(\frac1{15}\right)+f\left(\frac2{15}\right)+\dots+f\left(\frac{59}{15}\right)\right)$ is equal to

Explanation

Reviewed by Dr. Abubacker

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