# More help with induction!

• May 27th 2011, 09:57 AM
Timsworth
More help with induction!
I have no trouble with proving something by induction when I have a 'sum of' equation and an element equation, but I have no idea where to start with this:

Show that \$\displaystyle m_n = 2^n - 1\$ by induction for all \$\displaystyle n \geq 1\$

I have notes, but I can't make any sense out of them.

Can someone help me out in understanding the process for this question?

Cheers.
• May 27th 2011, 10:30 AM
TKHunny
• May 27th 2011, 10:35 AM
bryangoodrich
What \$\displaystyle m_n\$ supposed to be?
• May 27th 2011, 10:49 AM
Timsworth
Okay, I'm an idiot. I missed some seriously crucial information and now I understand.
This has been tripping me up for over an hour now -.- So simple.

\$\displaystyle m_{n+1} = 2m_n + 1\$

Show that \$\displaystyle m_n = 2^n - 1\$ by induction for all \$\displaystyle n \geq 1\$

\$\displaystyle n = 1 : m_n = 2^n - 1 = 1\$
\$\displaystyle m_{n+1} = 2m_n + 1\$
\$\displaystyle m_{n+1} = 2(2^n - 1) + 1\$
\$\displaystyle m_{n+1} = 2^{n+1} - 1\$

Cheers guys.