ta gọi biểu thức trên là B có
2B=2.(\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)+....+\(\frac{1}{4950}\))
2B=\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+......+\frac{1}{9900}\)
2B=\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.......+\frac{1}{99.100}\)
2B=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)+.....+\(\frac{1}{99}-\frac{1}{100}\)
2B=\(\frac{1}{3}-\frac{1}{100}\)
2B=\(\frac{100-3}{300}\)
B=\(\frac{97}{300}\): 2
B=\(\frac{97}{300}.\frac{1}{2}\)
B=\(\frac{97}{600}\)
Ta gọi biểu thức là A
A=1/6 + 1/10 + 1/15 + .... + 1/4950
A=6/12+6/20+6/30+...+6/9900
A=6.(1/3.4 + 1/4.5 + 1/5.6 +.... + 1/99.100 )
A=6.(1/3 - 1/4 +1/4-1/5+1/5-1/6+....+1/99-1/100)
A=6.(1/3-1/100)
A=6.97/300
A=97/50
\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{4950}\)
\(=\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{9900}\)
\(=\frac{2}{3\times4}+\frac{2}{4\times5}+\frac{2}{5\times6}+...+\frac{2}{99\times100}\)
\(=2\times\left(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{99\times100}\right)\)
\(=2\times\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=2\times\left(\frac{1}{3}-\frac{1}{100}\right)\)
\(=2\times\frac{97}{300}\)
\(=\frac{97}{150}\)
_Chúc bạn học tốt_
