Tính hợp lý:
\(B=\left(\frac{1}{212}\right)^2-\frac{1}{212}.\left(-\frac{211}{212}+\frac{1}{379}\right)+\frac{1}{379}.\left(\frac{1}{212}-1\right)-\frac{213}{212}\)
m.n giúp nhé
tìm các số nguyên x :
\(\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\right).420-\left[0.4.\left(0.75-2.5x\right)\right].4=212\)
rút gọn biểu thức N= \(12\left(\sqrt{2}-3\sqrt{18}+212\sqrt{8}\right):\sqrt{2}\)
N=\(\frac{5-\sqrt{5}}{\sqrt{5-1}}-\frac{4}{\sqrt{5+1}}\)
Tính hợp lý:
\(A=\left(3+\frac{1}{2}-\frac{2}{3}\right)-\left(2-\frac{2}{3}+\frac{5}{2}\right)+\left(-5+\frac{5}{2}-\frac{4}{3}\right)\)
\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{1.2}+...+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
M.n giúp mk vs
\(A=\left(3+\frac{1}{2}-\frac{2}{3}\right)-\left(2-\frac{2}{3}+\frac{5}{2}\right)+\left(-5+\frac{5}{2}-\frac{4}{3}\right)\)
\(=3+\frac{1}{2}-\frac{2}{3}-2+\frac{2}{3}-\frac{5}{2}-5+\frac{5}{2}-\frac{4}{3}\)
\(=\left(3-2-5\right)+\left(\frac{1}{2}-\frac{5}{2}+\frac{5}{2}\right)-\left(\frac{2}{3}-\frac{2}{3}+\frac{4}{3}\right)\)
\(=-4-\frac{1}{2}\)
\(=-\frac{9}{2}\)
\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
\(A=\left(3+\frac{1}{2}-\frac{2}{3}\right)-\left(2-\frac{2}{3}+\frac{5}{2}\right)+\left(-5+\frac{5}{2}-\frac{4}{3}\right)\)
\(A=3+\frac{1}{2}-\frac{2}{3}-2+\frac{2}{3}-\frac{5}{2}-5+\frac{5}{2}-\frac{4}{3}\)
\(A=\left(3-2-5\right)+\left(\frac{1}{2}-\frac{5}{2}+\frac{5}{2}\right)-\left(\frac{2}{3}-\frac{2}{3}+\frac{4}{3}\right)\)
\(A=-4+\frac{1}{2}-\frac{4}{3}\)
\(A=-\frac{29}{6}\)
Tính hợp lý
a, \(\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)............\left(\frac{1}{100^2}-1\right)\)
b, \(1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{5}}}}}\)
làm được câu nào thì giúp mình nhé , nói cả cách làm nữa nhé ^_^
Giải chi tiết giúp mk bài này với: Tính hợp lý :
\(A=\left(-\frac{2}{9}\right)-\left(-\frac{1}{121}\right)+\left(-\frac{3}{5}\right)+\left(-\frac{1}{2}\right)-\left(-1\frac{13}{18}\right)-\frac{1}{7}-\frac{9}{35}\)
\(B=0,75+\frac{3}{5}+\left(\frac{2}{9}-1\frac{3}{5}+1\frac{1}{4}\right)\)
\(C=1-2+3-4+...+79-80\)
c) C = ( 1 - 2 ) + ( 3 - 4 ) + ... + ( 79 - 80 )
C = ( -1 ) + ( -1 ) + ... + ( -1 )
C = ( -1 ) x ( 80 - 1 + 1 ) : 2
C = ( -1 ) x 80 : 2
C = ( -40 )
C=1-2+3-4+...+79-80
=(1-2)+(3-4)+...+(79-80)
=-1+(-1)+...+(-1) (có 80 số hạng bàng -1)
=-1*80
=-80
Tinhs giá trị biểu thức
a, A= \(\frac{sin33}{cos57}\)+\(\frac{tan32}{cotg58}\)- 2 \(\left(sin20cos70+cos20sin70\right)\)
b,B=\(\frac{sin^215+sin^275-sin^212-sin^278}{cos^213+cos^277+cos^21+cos^289}\)+ \(\frac{2tan55}{cotg35}\)
\(A=\frac{\cos57}{\cos57}+\frac{\cot58}{\cot58}-2\left(1+1\right)\)\()\)
=1+1-4
=-2
tính hợp lý :
tính hợp lý:\(\left(-1-\frac{1}{12}\right).\left(-1-\frac{1}{13}\right).\left(-1-\frac{1}{14}\right)......\left(-1-\frac{1}{2017}\right)\)
\(\left(-1-\frac{1}{12}\right).\left(-1-\frac{1}{13}\right).\left(-1-\frac{1}{14}\right)...\left(-1-\frac{1}{2017}\right)\)
\(=\frac{-13}{12}.\frac{-14}{13}.\frac{-15}{14}...\frac{-2018}{2017}\)
\(=\frac{-13}{12}.\frac{14}{-13}.\frac{-15}{14}...\frac{2018}{-2017}\)
\(=\frac{\left(-13\right).14.\left(-15\right)...2018}{12.\left(-13\right).14...2017}=\frac{2018}{12}=\frac{1009}{6}\)
Tính hợp lý
\(\left(\frac{-1}{2}\right)-\left(\frac{-3}{5}\right)+\left(\frac{-1}{9}\right)+\frac{1}{127}-\left(+\frac{7}{18}\right)+\frac{4}{35}-\left(\frac{-2}{7}\right)\)
\(=\left(-\frac{1}{2}-\frac{1}{9}-\frac{7}{18}\right)+\left(\frac{3}{5}+\frac{2}{7}+\frac{4}{35}\right)+\frac{1}{127}\)
\(=\left(-\frac{9}{18}-\frac{2}{18}-\frac{7}{18}\right)+\left(\frac{21}{35}+\frac{10}{35}+\frac{4}{35}\right)+\frac{1}{127}\)
\(=\left(-\frac{18}{18}\right)+\frac{35}{35}+\frac{1}{127}\)
\(=-1+1+\frac{1}{127}\)
\(=\frac{1}{127}\)
TÍNH HỢP LÝ
B=\(\left(\frac{2}{2.3}-1\right)\left(\frac{2}{3.4}-1\right)\left(\frac{2}{4.5}-1\right)...\left(\frac{2}{2008.2009}-1\right)\)
\(B=\left(\frac{2}{2.3}-1\right)\left(\frac{2}{3.4}-1\right)...\left(\frac{2}{2008.2009}-1\right)\)
\(B=\left(\frac{2}{2.3}-\frac{6}{2.3}\right)\left(\frac{2}{3.4}-\frac{12}{3.4}\right)...\left(\frac{2}{2008.2009}-\frac{2008.2009}{2008.2009}\right)\)
\(B=\left(-\frac{4}{2.3}\right)\left(-\frac{10}{3.4}\right)...\left(\frac{2-2008.2009}{2008.2009}\right)\)
\(B=\left(-\frac{1.4}{2.3}\right)\left(-\frac{2.5}{3.4}\right)...\left(-\frac{2007.2010}{2008.2009}\right)\)
Biểu thức B có (2008 - 2) : 1 + 1 = 2007 (thừa số)
Vì cả 2007 thừa số của biểu thức B đều mang dấu (-)
Nên biểu thức B mang dấu (-)
\(B=-\frac{1.2....2007}{2.3...2008}.\frac{4.5...2010}{3.4...2009}\)
\(B=-\frac{1}{2008}.\frac{2010}{3}\)
\(B=-\frac{1.2010}{2008.3}=-\frac{1.1005}{1004.3}=-\frac{1.335}{1004.1}\)
\(B=-\frac{335}{1004}\)
Vậy\(B=-\frac{335}{1004}\)