# How do you evaluate the series #Sigma 5r# from r=3 to 8?

We seek:

Due to the small number of terms required we can just expand the individual terms to get:

If the number of individual terms were larger this would be quite cumbersome and use of the standard summation formula

would be more appropriate. If we used this approach we would get

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To evaluate the series ( \sum_{r=3}^{8} 5r ), you would sum up the terms of the series by plugging in each value of ( r ) from 3 to 8 into the expression ( 5r ), and then adding up the results.

( \sum_{r=3}^{8} 5r = 5(3) + 5(4) + 5(5) + 5(6) + 5(7) + 5(8) )

( = 15 + 20 + 25 + 30 + 35 + 40 )

( = 165 )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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