Question

Tính nhanh:a)1/6+1/12+1/20+....+1/90

b)4/2.4+4/4.6+4/6.8+4/8.10+....+4/16.18+4/18.20

c)2/3+2/15+2/35+2/63

d)1995.1994-1/1993.1995+1994

Các bạn giúp mình với mình cảm ơn rất nhiều

Sáng mai mình phải nộp bài mong các bạn giúp đỡ

Answer 1

$a)\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{90}$

$=\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}$

$=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}$

$=\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{2}{5}$

Answer 2

b) Đặt $B=\dfrac{4}{2.4}+\dfrac{4}{4.6}+...+\dfrac{4}{18.20}$

$=>\dfrac{1}{2}B=\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{18.20}$

$=>\dfrac{1}{2}B=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{18}-\dfrac{1}{20}$

$=>\dfrac{1}{2}B=\dfrac{1}{2}-\dfrac{1}{20}=\dfrac{9}{20}$

$=>B=\dfrac{9}{10}$

c) $\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}$

$=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}$

$=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}$

$=1-\dfrac{1}{9}=\dfrac{8}{9}$

d) Viết lại đề rõ ràng nha bạn.