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How do you evaluate #\frac { 1} { 2} \sum _ { k = 1} ^ { 3} \frac { 2} { k }#?

Answer 1

Theodore Amidon

# 1/2 \ sum_(k=1)^3 \ 2/k = 11/6 #

With a small number of terms we can just write out those terms and evaluate the sum: Thus

# 1/2 \ sum_(k=1)^3 \ 2/k =1/2{2/1+2/2+2/3 } # # " " =1/2{2+1+2/3 } # # " " =1/2{11/3 } # # " " =11/6 #

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Answer 2

Cora Alexander

To evaluate ( \frac{1}{2} \sum_{k=1}^{3} \frac{2}{k} ), first find the sum of the fractions for each value of ( k ) from 1 to 3, then divide the sum by 2.

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Answer from HIX Tutor

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.