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\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\right)^2+\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\right)\cdot \frac{1}{2}-\left(1+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\right)\cdot \left(\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\right)

 Sep 11, 2020
 #1
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+1

(1/2 + 2/3 + 3/4 + 4/5)^2 + (1/2 + 2/3 + 3/4 + 4/5) *1/2 - (1 + 1/2 + 2/3 + 3/4 + 4/5) * (2/3 + 3/4 + 4/5)=

 

[26569 / 3600] + [163 / 120] - [223 / 60 * 133 / 60]

 

[31459 / 3600]            -              [29659 / 3600]

 

1800 / 3600 = 1/2 - which is the final answer.

 Sep 11, 2020

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