Câu hỏi của Nguyễn Thị Ánh Ngọc

Question

a)6/1.4+6/4.7+6/7.10+....+6/97.100

b 4/1.3+16/3.5+36/5.7+.....+9604/97.99

c (1/1.2+1/3.4+1/5.6+...........+1/19.20)-(1/11+1/12+.....+1/20)

tthnew · Accepted Answer

a)Đặt $A=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+...+\dfrac{6}{97.100}$

$3a=3-\dfrac{3}{4}+\dfrac{3}{4}-\dfrac{3}{7}+\dfrac{3}{7}-\dfrac{3}{10}+...+\dfrac{3}{97}-\dfrac{3}{100}$

$=3-\dfrac{3}{100}$

$=\dfrac{297}{100}$

b)Đặt $B=\dfrac{4}{1.3}+\dfrac{16}{3.5}+\dfrac{36}{5.7}+...+\dfrac{9604}{97.99}$

$=2b=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}$

$2b=2-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{97}-\dfrac{2}{99}$

$2b=2-\dfrac{2}{99}=\dfrac{198}{99}-\dfrac{2}{99}=\dfrac{196}{99}$

c) Tương tự! Bạn tự làm nhé!Câu trả lời: a)Đặt $A=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+...+\dfrac{6}{97.100}$