Question

Bài 1:Tính bằng cách hợp lý:

a)\(\frac{8.4.125.25+96524+3476}{1+5+9+...+61+62,5-26}\)

b)\(\frac{5+55+555+5555}{9+99+999+9999}\)

c)39,2.27+39,2.43+78,4.15

d)\(\frac{4}{17}.\frac{3}{11}+\frac{8}{11}.\frac{4}{17}-\frac{4}{17}\)

e)(812,1.10,5-91.10,5).(41.11-4100.0,1-41)

Bài 2:Tính nhanh các tổng sau:

a)\(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{57.59}\)

b)\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\right)-\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)\)

c)\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right)\cdot...\cdot\left(1-\frac{1}{2012}\right)\)

GẤP!GẤP!GẤP!MAI MIK NỘP RỒI!BẠN NÀO ĐẦU TIÊN MIK TIK CHO NHA!

*Lưu ý:Dấu chấm là dấu nhân đó

 

 

 

 

Answer 1

Bài 1. 

b) \(\frac{5+55+555+5555}{9+99+999+9999}\)

= \(\frac{5\left(1+11+111+1111\right)}{9\left(1+11+111+1111\right)}=\frac{5}{9}\)

c) \(39,2\cdot27+39,2\cdot43+78,4\cdot15\)

= \(39,2\cdot27+39,2\cdot43+39,2\cdot2\cdot15\)

= \(39,2\left(27+43+30\right)=39,2\cdot100=3920\)

d) \(\frac{4}{17}\cdot\frac{3}{11}+\frac{8}{11}\cdot\frac{4}{17}-\frac{4}{17}\)

= \(\frac{4}{17}\left(\frac{3}{11}+\frac{8}{11}-1\right)=\frac{4}{17}\cdot0=0\)

Bài 2.

a) \(\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+...+\frac{1}{57\cdot59}\)

= \(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{57}-\frac{1}{59}\)

= \(\frac{1}{5}-\frac{1}{59}=\frac{54}{295}\)

b) \(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\right)-\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)\)

= \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}-\frac{1}{3}-\frac{1}{4}-\frac{1}{5}-\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\)

= \(\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

c) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)...\left(1-\frac{1}{2012}\right)\)

= \(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{2011}{2012}=\frac{1}{2012}\)