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S = \(\frac{1}{2}\)+ \(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{24}\)+\(\frac{1}{48}\)
S = \(\frac{24}{48}\)+ \(\frac{8}{48}\)+\(\frac{4}{48}\)+\(\frac{2}{48}\)+\(\frac{1}{48}\)
S = \(\frac{39}{48}\)= \(\frac{13}{16}\)
\(\Rightarrow\)S = \(\frac{13}{16}\)
28+62.a.(a.1-a:1)+28.8+28
=(28+28+28.8)+62.a.(a-a)
=(28.10)+62.a.0
=280+0
=280
28+62.a.(a.1-a:1)+28.8+28
=28.10+62.a.(a-a)
=280+62.a.0
=280
\(=2\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)
\(=2\left(1-\frac{1}{192}\right)\)
\(=2\times\frac{191}{192}\)
\(=\frac{191}{96}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(=\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{12}+\frac{1}{24}\right)+\left(\frac{1}{48}+\frac{1}{96}\right)\)
\(=\frac{1}{2}+\frac{1}{8}+\frac{1}{32}\)
\(=\frac{21}{32}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
= \(\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{12}+\frac{1}{24}\right)+\left(\frac{1}{48}+\frac{1}{96}\right)+\frac{1}{192}\)
= \(\left(\frac{1}{2}+\frac{1}{8}\right)+\left(\frac{1}{32}+\frac{1}{192}\right)\)
= \(\frac{5}{8}+\frac{1}{192}\)
= \(\frac{121}{192}\)
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