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

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Answer 1 · 2017-05-08T17:03:09

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

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

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

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