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

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Homework Help Overview

The problem involves summing a series of squared terms in the form of (18n-1)^2, specifically (5^2) + (11^2) + (17^2) +... The participants are tasked with expressing this sum in sigma notation and using sigma identities to evaluate it.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the correct form of the sigma notation, with one suggesting ∑ (6n-1)^2 and questioning the bounds of summation. There is uncertainty about whether to sum from 1 to k or from 1 to 3k, with attempts to clarify the correct limits for the series.

Discussion Status

There is an ongoing exploration of the correct sigma notation and bounds for the summation. Some participants express confusion about the transition from the sigma notation to the evaluation of the sum, indicating that they are working through the problem collaboratively without reaching a consensus.

Contextual Notes

Participants mention a lack of recent experience with induction and sigma identities, which may be affecting their confidence in determining the correct approach. There is also a specific reference to needing the sum to align with a particular expression for part b, which adds complexity to the discussion.

Liquidxlax
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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
 
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Liquidxlax said:

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.)
 
Liquidxlax said:
∑ (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.
 
haruspex said:
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
 

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