Answer
$5\dfrac {71}{105} $
$\approx 0.676 $
Work Step by Step
$\sum ^{4}_{i=1}\dfrac {2i}{2i-1}=\sum ^{4}_{i=1}\dfrac {2i-1+1}{2i-1}=\sum ^{4}_{i=1}\left( 1+\dfrac {1}{2i-1}\right) =4+\sum ^{4}_{i=1}\dfrac {1}{2i-1}=4+\dfrac {1}{2\times 1-1}+\dfrac {1}{2\times 2-1}+\dfrac {1}{2\times 3-1}+\dfrac {1}{2\times 4-1}=4+\dfrac {1}{1}+\dfrac {1}{3}+\dfrac {1}{5}+\dfrac {1}{7}=5+\dfrac {5\times 7+3\times 7+5\times 3}{5\times 7\times 3}=5+\dfrac {71}{105} $
