# Mathematical induction

1. Jan 26, 2014

### Liquidxlax

1. The problem statement, all variables and given/known data
(5^2) + (11^2) + (17^2) +...+ (18n-1)^2

a)Write the sum in sigma notation
b)Using the sigma identities solve the sum (easy to do)

2. Relevant equations

∑i = .5*k*(k+1) etc

3. The attempt at a solution

The problem i'm having is with the 25 and 121. I thought it was

∑ (6n-1)^2

where n goes from 1 to k,
but I noticed that this does not work for part b then.
I haven't done induction in 4 years, so unfortunately I forget.

Unless it isn't from 1 to k, but from 1 to 3k

2. Jan 26, 2014

### SammyS

Staff Emeritus
How about each term is of the form (6k - 1)^2 ...

Then k has k go from 1 to ___ . (Fill in the blank.)

3. Jan 26, 2014

### haruspex

Yes

4. Jan 27, 2014

### Liquidxlax

yeah it does go from 1 to 3k, not 1 to k because it needs to be for part b equal to

3n(108n^2 +36n +1)

Where i was stuck was knowing the bounds

Prove $5^n+9<6^n$ for $n\epsilon N|n\ge2$ by induction Jun 9, 2017