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a; 5\(\dfrac{3}{4}\) : 3 + 2\(\dfrac{1}{4}\).\(\dfrac{1}{3}\) - \(\dfrac{3}{8}\)
= \(\dfrac{23}{4}\) : 3 + \(\dfrac{9}{4}\).\(\dfrac{1}{3}\) - \(\dfrac{3}{8}\)
= \(\dfrac{23}{4}\) x \(\dfrac{1}{3}\) + \(\dfrac{3}{4}\) - \(\dfrac{3}{8}\)
= \(\dfrac{23}{12}\) + \(\dfrac{3}{4}\) - \(\dfrac{3}{8}\)
= \(\dfrac{46}{24}\) + \(\dfrac{18}{24}\) - \(\dfrac{9}{24}\)
= \(\dfrac{64}{24}\) - \(\dfrac{9}{24}\)
= \(\dfrac{55}{24}\)
Tính bằng cách thuận tiện nhất:
1-1/5 × 1-1/6 × 1-1/7 × 1-1/8 × ...× 1-1/100.
Mọi người giúp với!!!!!!
\(1-\frac{1}{5}\times1-\frac{1}{6}\times.....\times1-\frac{1}{100}\)
\(=\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times.....\times\frac{99}{100}\)
\(=\frac{4\times5\times....\times99}{5\times6\times...\times100}\)
\(=\frac{1}{25}\)
Ta có: \(\left(1-\frac{1}{5}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{8}\right)...\left(1-\frac{1}{100}\right)\)
\(=\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot...\cdot\frac{98}{99}\cdot\frac{99}{100}\)
\(=\frac{4}{100}=\frac{1}{25}\)
\(\frac{4}{3}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}:\frac{9}{8}\)
=\(\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)
=\(\frac{16}{27}\)
A = \(\dfrac{5}{2}\) + \(\dfrac{5}{4}\) +\(\dfrac{5}{8}\) + \(\dfrac{5}{16}\) + ....+\(\dfrac{5}{512}\)+\(\dfrac{5}{1024}\)
2.A = 5+ \(\dfrac{5}{2}\) + \(\dfrac{5}{4}\)+ \(\dfrac{5}{8}\)+ \(\dfrac{5}{16}\)+.......+\(\dfrac{5}{512}\)
2A - A = 5 - \(\dfrac{5}{1024}\)
A = \(\dfrac{5115}{1023}\)