0

So I have the equation https://puu.sh/uosqs/d90b94c2f5.png

$\sum_{i=0}^{h}m^i=v$ and I need to solve for $h$. How do I rearrange this equation so that it is in the form $h$ = something?

Pawel
  • 4,871
Malingos
  • 5
  • $h$ tells you how many terms are in the sum. In your case, $\sum_{i=0}^{h}m^i=v$ means $m^0+m^1+...+m^h=v$ Try using this fact to solve for $h$. – Pawel Mar 01 '17 at 01:26

1 Answers1

1

You can't rearrange summations to solve for their bounds, but you can solve the summations themselves. What you have is a geometric series, which means

$$\frac{m^{h+1}-1}{m-1}=\sum_{i=0}^hm^i=v$$

Thus,

$$m^{h+1}-1=v(m-1)\\m^{h+1}=v(m-1)+1\\h+1=\log_m[v(m-1)+1]$$

$$h=\log_m[v(m-1)+1]-1$$

Simply Beautiful Art
  • 74,685