Làm lại câu a
\(2S=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)
\(2S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(2S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(2S=1-\frac{1}{100}\)suy ra \(2S=\frac{99}{100}\)
\(S=\frac{99}{100}:2\)suy ra \(S=\frac{99}{200}\)
a, 2S=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)
\(2S=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{100}\)
\(2S=1-\frac{1}{100}\)suy ra \(2S=\frac{99}{100}\)
\(S=\frac{99}{100}:2=\frac{99}{200}\)
Ta có 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/98.99.100
= 1/2 ( 1 / 1.2 - 1 / 2.3 + 1 / 2.3 - 1 / 3.4 + ...................+ 1 / 97.98 - 1 / 98.99 + 1 / 98.99 - 1 / 99.100)
= 1 / 2 ( 1 / 1.2 - 1 / 99.100 )
= 4949 / 19800