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Math Help - An expression for a sum

  1. #1
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    Question An expression for a sum

    Hi, I am going through some calculus questions and came across this particular question which I don't really understand. It says:
    Consider the sum

    We haven't spent a great deal of time on summations in lectures, so I was quite confused how to approach this, as isn't the sigma the expression for this sum... Any help would be greatly appreciated.
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    Quote Originally Posted by macduff View Post
    Hi, I am going through some calculus questions and came across this particular question which I don't really understand. It says:
    Consider the sum

    We haven't spent a great deal of time on summations in lectures, so I was quite confused how to approach this, as isn't the sigma the expression for this sum... Any help would be greatly appreciated.
    Are you familiar with the summation notation? This might help:

    In long hand the expression is

    (3(1) - 1) + (3(2) - 1) + (3(3) - 1) + (3(4) - 1) + .... + (3(n) - 1)

    = (3 - 1) + (6 - 1) + (9 - 1) + (12 - 1) + .... + (3n - 1)

    = 2 + 5 + 8 + 11 + .... + 3n - 1
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    Sorry, I didn't post the end of the question, it was supposed to say find and expression for this sum. Thats why I am so confused because the sum is 2 + 5 + 8 + 11 + .... + 3n - 1 so isn't the expression of the sum the summation notation? Maybe the original question in the book has a typo in it...
    Quote Originally Posted by mr fantastic View Post
    Are you familiar with the summation notation? This might help:

    In long hand the expression is

    (3(1) - 1) + (3(2) - 1) + (3(3) - 1) + (3(4) - 1) + .... + (3(n) - 1)

    = (3 - 1) + (6 - 1) + (9 - 1) + (12 - 1) + .... + (3n - 1)

    = 2 + 5 + 8 + 11 + .... + 3n - 1
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  4. #4
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    Quote Originally Posted by macduff View Post
    Sorry, I didn't post the end of the question, it was supposed to say find and expression for this sum. Thats why I am so confused because the sum is 2 + 5 + 8 + 11 + .... + 3n - 1 so isn't the expression of the sum the summation notation? Maybe the original question in the book has a typo in it...
    \sum_{j=1}^n (3j - 1) = 3 \left( \sum_{j=1}^n j \right) - \sum_{j=1}^n 1 = 3 \cdot \frac{n(n+1)}{2} - n.

    The simplification of this answer is left for you to do.

    The research of the formula I used is left for you to do eg. How to Sum the Integers from 1 to N - wikiHow
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  5. #5
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    Thanks!
    Quote Originally Posted by mr fantastic View Post
    \sum_{j=1}^n (3j - 1) = 3 \left( \sum_{j=1}^n j \right) - \sum_{j=1}^n 1 = 3 \cdot \frac{n(n+1)}{2} - n.

    The simplification of this answer is left for you to do.

    The research of the formula I used is left for you to do eg. How to Sum the Integers from 1 to N - wikiHow
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