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\(A=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{20}+\dfrac{1}{40}+\dfrac{1}{80}+\dfrac{1}{160}\\ A=\dfrac{35}{160}+\dfrac{16}{160}+\dfrac{8}{160}+\dfrac{4}{160}+\dfrac{2}{160}+\dfrac{1}{160}\\ A=\dfrac{66}{160}\\ A=\dfrac{33}{80}.\)
A = 1/5 + 1/10 + 1/20 + 1/40 + ..... + 1/1280
A x 2 = 2/5 - ( 1 /5 + 1/10 + 1/20 + 1/40 + ... + 1/1280 ) - 1/1280
A x 2 = 2/5 - A - 1/1280
A x 2 - A = 2/5 - 1/1280
A = 2/5 - 1/1280
A = 511/1280
A = 1/5 + 1/10 + 1/20 + 1/40 + ..... + 1/1280
A x 2 = 2/5 - ( 1 /5 + 1/10 + 1/20 + 1/40 + ... + 1/1280 ) - 1/1280
A x 2 = 2/5 - A - 1/1280
A x 2 - A = 2/5 - 1/1280
A = 2/5 - 1/1280
A = 511/1280
12/20=6/10=3/5
24/36=8/12=
3/4=9/12=12/16=15/20
2/5=4/10
12/30=4/10
72/45=8/5
1/4=7/28
= 5/6 x 6/7 x 7/8 x 8/9 x 9/10
= 5/10
= 1/2
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\(\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{10}\right)\)
\(=\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\times\frac{9}{10}\)
\(=\frac{5\times6\times7\times8\times9}{6\times7\times8\times9\times10}\)
\(=\frac{5}{10}=\frac{1}{2}\)
\(\frac{1}{2}+\frac{1}{3}+\frac{5}{9}\)
MSC : 18
\(\frac{1}{2}+\frac{1}{3}+\frac{5}{9}=\frac{9}{18}+\frac{6}{18}+\frac{10}{18}=\frac{25}{18}\)
\(\frac{10}{3}-\left(\frac{1}{4}+\frac{1}{12}\right)\)
\(=\frac{10}{3}-\frac{1}{4}-\frac{1}{12}\)
\(=\frac{40}{12}-\frac{3}{12}-\frac{1}{12}\)
\(=\frac{36}{12}=3\)
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