\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)
\(=\)\(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)
\(=\)\(\frac{9}{3}\)
\(=\)\(3\)
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)
\(=\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)
Rút gọn phép tính trên ta được :
\(=\frac{9}{3}=3\)
A=1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+....+1(x+99)(x+100)A=1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+....+1(x+99)(x+100)
=1x−1x+1+1x+1−1x+2+1x+2−1x+3+....+1x+99−1x+ 100=1x-1x+1+1x+1-1x+2+1x+2-1x+3+....+1x+99-1x+ 100
=1x−1x+100=1x-1x+100
=x+100−xx(x+ 100)=x+100-xx(x+ 100)
=100x(x+100)
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