How Do You Sum a Series Using Sigma Notation and Identities?

[Liquidxlax]

Homework Statement

(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)

Homework Equations

∑i = .5*k*(k+1) etc

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

 

[SammyS]

Homework Statement

(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)

Homework Equations

∑i = .5*k*(k+1) etc

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

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

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

 

[haruspex]

∑ (6n-1)^2
where n goes from 1 to k,

Yes

but I noticed that this does not work for part b then.

It doesn't? I don't see your difficulty. Please post your working up to where you're stuck.

 

[Liquidxlax]

Yes
It doesn't? I don't see your difficulty. Please post your working up to where you're stuck.

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