S=1/51.10+1/10.15+…+1/95.100 CM S<1 Tính A=2/1.4+2/4.7+2/7.10+...+2/97.100 Help me

0 bình luận về “S=1/51.10+1/10.15+…+1/95.100 CM S<1 Tính A=2/1.4+2/4.7+2/7.10+...+2/97.100 Help me”

1. câu 1

   s=5/5×1(1/5.10+1/10.15+…+1/95.100)

   s=1/5×5/5.10+5/10.15+…+5/95.100

   s=1/5×1/1-1/10+1/10-1/15+1/95-1/100

   s=1/5×1/1-1/100

   s=1/5×99/100

   s=99/500

   vì 99/100=0,99 nên s<1

   câu 2

   A=2/1.4+2/4.7+2/7.10+…+2/97.100

   A=3/3×2(1/1.4+1/4.7+1/7.10+…+1/97.100)

   A=2/3×3/1.4+3/4.7+3/7.10+…+3/97.100)

   A=2/3×1/1-1/4+1/4-1/7+….+1/97-1/100

   A=2/3×1/1-1/100

   A=2/3×99/100

   A=198/300

   pls give me vote

   Trả lời

2. $1)S=\dfrac{1}{5.10}+\dfrac{1}{10.15}+\cdots+\dfrac{1}{95.100}\\ 5S=\dfrac{5}{5.10}+\dfrac{5}{10.15}+\cdots+\dfrac{5}{95.100}$

   Ta thấy:

   $\dfrac{5}{5.10}=\dfrac{1}{5}-\dfrac{1}{10}\\ \dfrac{5}{10.15}=\dfrac{1}{10}-\dfrac{1}{15}\\ \cdots\\ \dfrac{5}{95.100}=\dfrac{1}{95}-\dfrac{1}{100}\\ \Rightarrow 5S=\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+\cdots+\dfrac{1}{95}-\dfrac{1}{100}\\ =\dfrac{1}{5}-\dfrac{1}{100}\\ =\dfrac{19}{100}\\ \Rightarrow S=\dfrac{19}{500}<1\\ 2)S=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\cdots+\dfrac{2}{97.100}\\ \dfrac{3}{2}S=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\cdots+\dfrac{3}{97.100}\\ =1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\cdots+\dfrac{1}{97}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\\ \Rightarrow S=\dfrac{33}{50}$

   Trả lời