10000:2
1000:2
100:2
10:2
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12/84 + 12/210 + 12/390 + ...+12/2100
= 4/28 + 4/70 + 4/130 + ...+ 4/700
= 4/4.7 + 4/7.10 + 4/10.13 + ... + 4/25.28
= (3/4.7 + 3/7.10 + 3/10.13 + ...+ 3/25.28).4/3
= (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/25 - 1/28).4/3
= (1/4 - 1/28) .4/3
= (7/28 - 1/28).4/3
= 6/28 . 4/3
= 3.2.4/7.4.3
= 2/7
\(\dfrac{6}{84}+\dfrac{6}{210}+\dfrac{6}{390}+...+\dfrac{6}{2100}\)
\(=\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+...+\dfrac{2}{700}\)
\(=\dfrac{2}{4.7}+\dfrac{2}{7.10}+\dfrac{2}{10.13}+...+\dfrac{2}{25.28}\)
\(=\dfrac{2}{3}.\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\right)\)
\(=\dfrac{2}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{2}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{1}{7}\)
10000 : 2 = 5000
1000 : 2 = 500
100 : 2 = 50
10 : 2 = 5
10000 : 2 = 5000
1000 : 2 = 500
100 : 2 = 50
10 : 2 = 5