Question

[nguyen thi quynh huong]

Tính nhanh:

a) \(\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+\frac{3^2}{10.13}+\frac{3^2}{13.16}+...+\frac{3^2}{97.100}\)

b)\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{940}\)

c) A= \(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+\frac{6}{130}+\frac{6}{208}\)

d) M= \((1-\frac{1000}{2016}).(1-\frac{1001}{2016}).(1-\frac{1002}{2016})...(1-\frac{2017}{2016})\)

e) A= \(8400.(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+\frac{1}{17.21}+\frac{1}{21.25})\)

f) T= \((\frac{1}{2}+1).(\frac{1}{3}+1).(\frac{1}{4}+1)...(\frac{1}{98}+1).(\frac{1}{99}+1)\)

h) A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)phần \(\frac{1}{5}+\frac{5}{3}+\frac{5}{6}+\frac{1}{2}+...+\frac{1}{9}\)

Answer 1

[Trường]

c)  \(A=\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+\frac{6}{130}+\frac{6}{208}\) 

\(=\frac{6}{1.4}+\frac{6}{4.7}+\frac{6}{7.10}+\frac{6}{10.13}+\frac{6}{13.16}\) 

\(=2\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)

\(=2\left(1-\frac{1}{16}\right)\) 

\(=2.\frac{15}{16}\) 

\(=\frac{15}{8}\) 

Vậy A=\(\frac{15}{8}\)

Answer 2

[Kiệt Nguyễn]

a) \(\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+...+\frac{3^2}{97.100}\)

\(=3\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\right)\)

\(=3\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=3\left(1-\frac{1}{100}\right)\)

\(=3.\frac{99}{100}=\frac{297}{100}\)