Question

The largest term of the sequence $\frac{1}{503},\frac{4}{524},\frac{9}{581},\frac{16}{692},...$ is approximately:

• A. $\frac{49}{16}$
• B. $\frac{48}{1509}$
• C. $\frac{49}{1529}$
• D. $\frac{64}{1509}$

Answer 1

The correct option is C $\frac{49}{1529}$

$500+1\times 3500+8\times 3500+27\times 3500+64\times 3$

$y=T_r=\frac{r^2}{500+3r^3}$

$\frac{dy}{dr}=\frac{\left(500+3r^3\right)2r-r^2\left(0+9r^2\right)}{{\left(500+3r^3\right)}^2}=0$

$\left(500+3r^3\right)2r-9r^4=0$

$1000+6r^3-9r^3=0$

$1000=3r^3$

$r=6.93\cong 7$

$T_7=\frac{7^2}{500+3\times 7^3}=\frac{49}{1529}$