\(A=\dfrac{18}{2.5}+\dfrac{18}{5.8}+...+\dfrac{18}{203.206}\)
\(A=\dfrac{6.3}{2.5}+\dfrac{6.3}{5.8}+...+\dfrac{6.3}{203.206}\)
\(A=6\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+...+\dfrac{3}{203.206}\right)\)
\(A=6\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{203}-\dfrac{1}{206}\right)\)
\(A=6\left(\dfrac{1}{2}-\dfrac{1}{206}\right)\)
\(A=6.\dfrac{51}{103}\)
\(A=\dfrac{306}{103}\)
18/(2.5) + 18/(5.8) + .... + 18/(203.206)
= 18.[1/(2.5) + 1/(5.8) + .... + 1/(203.206)]
= 18.(1/2 - 1/5 + 1/5 - 1/8 + .... + 1/203 - 1/206)
=18.(1/2 - 1/206)
=18.(51/103)
=918/103
