A = 5(1/1.2 + 1/2.3 +......+ 1/99.100)
A = 5( 1 - 1/2 + 1/2 - 1/3 +........+ 1/99 - 1/100)
A = 5( 1 - 1/100)
A = 5 . 99/100
A = 99/20
** k mk nha!
\(\frac{5}{1\times2}+\frac{5}{2\times3}+...+\frac{5}{99\times100}=5\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\right)=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)=5\left(1-\frac{1}{100}\right)=5\times\frac{99}{100}=\frac{99}{20}=4\frac{19}{20}\)
A=5/1-5/2+5/2-5/3+...+5/99-5/100
A=5-(5/2-5/2+5/3-5/3+...5/99-5/99)-5/100
A=5-0+0+0+...+0-5/100
A=5-5/100
A=49/10=4,9
đặt 5 ra ngoài rồi làm nha :
\(5.\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}\right)\)
\(5\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
5.( \(\frac{1}{1}-\frac{1}{100}\))
tự làm tiếp nha
\(=5X\left(\frac{1}{1X2}+\frac{1}{2X3}+...+\frac{1}{98X99}+\frac{1}{99X100}\right)\)
\(=5X\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=5X\left(1-\frac{1}{100}\right)\)
\(=5X\frac{99}{100}\)
\(=\frac{99}{20}\)
