1. ## Discrete Maths question

What is the approximate value of c which minimises |a_100|?

Where a_n = (8+c)*2^n - (7+c)*3^n

Thank you for helping out!

2. Originally Posted by DaRush19
What is the approximate value of c which minimises |a_100|?

Where a_n = (8+c)*2^n - (7+c)*3^n

Thank you for helping out!
$\displaystyle |a_{100}|$ is minimised when $\displaystyle (8+c)\times 2^n=(7+c) \times 3^c$ when it is zero. Which is equivalent to:

$\displaystyle (8+c)=(7+c)(3/2)^{100}$

now rearrange:

$\displaystyle c=\frac{8-7(3/2)^{100}}{(3/2)^{100}-1}\approx -7$

CB

3. Thanks!