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Ta có 1/1.2-1/2.3=2/1.2.3;1/2.3-1/3.4=2/2.3.4 .....1/98.99-1/99.100=2/98.99.100 2A=2/1.2.3+2/2.3.4+....+2/98.99.100 = 1/1.2-1/2.3+1/2.3-1/3.4+...+1/98.99-1/99.100 = 1/2-1/99.100 = 4949/9900 A =4949/19800
Ta có: 2/1.3 = 1/1 - 1/3
2/3.5 = 1/3 - 1/5
\(\Rightarrow\) 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101
= 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
tích trên sẽ = 1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/100
=1-1/100 =99/100
bạn nhớ rằng k/n.(n+k) sẽ = 1/n-1/n+k
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+..+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
Ủng hộ mk nha !!! ^_^
Ta có: \(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
\(Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)\)
\(Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}\)
\(Q=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}\)
\(Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}\)
\(Q=100.\frac{2}{101}\)
\(Q=\frac{200}{101}\)
\(Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)\)
\(Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}\)
\(Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}\)
\(Q=100.\frac{2}{101}\)
\(Q=\frac{200}{101}\)