Sai Đề

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)..................\left(1-\frac{1}{20}\right)\)

=\(\frac{1}{2}.\frac{2}{3}.............\frac{19}{20}\) 

=\(\frac{1.2.3..............19}{2.3.4..............20}\) 

=\(\frac{1}{20}\)

\(B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{21}{20}\)

\(B=\frac{21}{2}\)

@@@

\(B=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{20}\right)\)

\(\Rightarrow B=\left(\frac{2}{2}+\frac{1}{2}\right)\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{4}{4}+\frac{1}{4}\right)...\left(\frac{20}{20}+\frac{1}{20}\right)\)

\(\Rightarrow B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)

\(\Rightarrow B=\frac{21}{2}\)

B=\(\left(1+\frac{1}{2}\right)\).\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\)...\(\left(1+\frac{1}{20}\right)\)

B=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)=\(\frac{21}{2}\)

vậy B= 21/2

Ta có:\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}=\frac{1}{20}\)

\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{19}{20}\)

\(=\frac{1\cdot2\cdot...\cdot19}{2\cdot3\cdot...\cdot20}\)

\(=\frac{1}{20}\)

\(B=\left[1-\frac{1}{2}\right]\cdot\left[1-\frac{1}{3}\right]\cdot\left[1-\frac{1}{4}\right]\cdot...\cdot\left[1-\frac{1}{20}\right]\)

\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{19}{20}\)

\(B=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}=\frac{1}{20}\)

@@@@@

Lời giải:

$A=1+\frac{2.3}{2.2}+\frac{3.4}{2.3}+\frac{4.5}{2.4}+...+\frac{20.21}{2.20}$

$=1+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}$

$=\frac{1+2+3+...+21}{2}-\frac{1}{2}=\frac{21.22}{2.2}-\frac{1}{2}=115$

B= \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\)\(\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

B= \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)= \(\frac{1}{20}\)

vậy B= \(\frac{1}{20}\)

b,A=(1/101+1/102+...+1/150)+(1/151+1/152+...1/200)>25/125+25/150+25/175+25/200=(1/5+1/6+1/7)+1/8=107/201+1/8>1/2+2/8=5/8

Vậy A>5/8

Nhớ k mik nha!!!!!!!!!!!!!

a/ Quy đồng mẫu số trong các ngoặc đơn, chúng sẽ giản ước được :\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{18}{19}.\frac{19}{20}=\frac{1}{20}.\) 

b/  Chứng minh   A> 5/8  

\(A=(\frac{1}{101}+...\frac{1}{125})+(\frac{1}{126}+...+\frac{1}{150})+(\frac{1}{151}+...+\frac{1}{175})+\left(\frac{1}{176}+...+\frac{1}{200}\right)\ge.\) 

         \(\ge\frac{25}{125}+\frac{25}{150}+\frac{25}{175}+\frac{25}{200}=\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}=\left(\frac{1}{5}+\frac{1}{7}\right)+\left(\frac{1}{6}+\frac{1}{8}\right)=\frac{12}{35}+\frac{7}{24}>\frac{24}{72}+\frac{21}{72}=\frac{45}{72}=\frac{5}{8}\)