\(S=\frac{2}{2.3}+\frac{2}{2.4}+\frac{2}{4.5}+.....+\frac{2}{99.100}\)
\(S=\frac{1}{2}.\left(\frac{2}{2}-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+......+\frac{2}{99}-\frac{2}{100}\right)\)
\(S=\frac{1}{2}.\left(\frac{2}{2}-\frac{2}{100}\right)\)
\(S=\frac{1}{2}.\left(1-\frac{1}{50}\right)\)
\(S=\frac{1}{2}.\frac{49}{50}\)
\(S=\frac{49}{100}\)
s=2/2x3+2/3x4+2/4x5+...+2/99x100
s=1/2x3+1/3x4+1/4x5+...+1/99x100
s=1/2-1/100
s=49/100
\(s=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{99.100}\)
=>\(s=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{99.100}\right)\)
=>\(S=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{99}-\frac{1}{100}\right)\)
=>\(S=2.\left(\frac{1}{2}-\frac{1}{100}\right)\)
=>\(S=2.\frac{49}{100}\)
=>\(S=\frac{49}{50}\)
ai k mình mình k lại
\(S=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{99\cdot100}=2\cdot\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}\right)\)
\(S=2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)=2\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(S=2\cdot\frac{49}{100}=\frac{49}{50}\)
