Chương I : Ôn tập và bổ túc về số tự nhiên
Các câu hỏi tương tự
1 .Tìm x biết
a. ( dfrac{1}{1.4}+dfrac{1}{4.7}+dfrac{1}{7.10}+...+dfrac{1}{97.100}) dfrac{0,33x}{2009}
b. 1 + dfrac{1}{3}+dfrac{1}{6}+dfrac{1}{10}+...+dfrac{2}{xleft(x+1right)}1dfrac{1991}{1993}
c. dfrac{1}{2013}x+1+dfrac{1}{2}+dfrac{1}{6}+dfrac{1}{12}+...+dfrac{1}{2012.2013}2
d. 2x + dfrac{7}{6}+dfrac{13}{12}+dfrac{21}{20}+dfrac{31}{30}+dfrac{43}{42}+dfrac{57}{56}+dfrac{73}{72}+dfrac{91}{90}10
2. Chứng minh rằng :
a. dfrac{1}{4}+dfrac{1}{4^2}+dfrac{1}{4^3}+...+dfrac{1}{4^{99}} dfrac{1}{3...
Đọc tiếp
1 .Tìm x biết
a. ( \(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{97.100}\)) = \(\dfrac{0,33x}{2009}\)
b. 1 + \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=1\dfrac{1991}{1993}\)
c. \(\dfrac{1}{2013}x+1+\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2012.2013}=2\)
d. 2x + \(\dfrac{7}{6}+\dfrac{13}{12}+\dfrac{21}{20}+\dfrac{31}{30}+\dfrac{43}{42}+\dfrac{57}{56}+\dfrac{73}{72}+\dfrac{91}{90}=10\)
2. Chứng minh rằng :
a. \(\dfrac{1}{4}+\dfrac{1}{4^2}+\dfrac{1}{4^3}+...+\dfrac{1}{4^{99}}< \dfrac{1}{3}\)
b. \(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{18.19.20}< \dfrac{1}{4}\)
Câu 1 : Thực hiện phép tính 1 cách hợp lý :
a) dfrac{-12}{7}.dfrac{4}{35}+dfrac{12}{7}.dfrac{left(-31right)}{35}-dfrac{2}{7}
b) 1+2-3-4+5+5-7-8+...+97+98-99-100
c) A157.left(-37right)-left(41.53-37.157right)+51.53
d) Bleft(dfrac{1}{11}+dfrac{1}{21}+dfrac{1}{31}+dfrac{1}{41}+dfrac{1}{51}right)left(dfrac{-41}{123}+dfrac{31}{-186}-dfrac{-51}{102}right)
Câu 2 :
a) 12 ( x - 5 ) 7x - 5
b) Tìm x in Z sao cho : ( 2x - 3 ) 2010 ( 2x - 3 ) 2012
Câu 3 :
1) Cho biểu thức S 1 + 3 + 32 + 33 +.....
Đọc tiếp
Câu 1 : Thực hiện phép tính 1 cách hợp lý :
a) \(\dfrac{-12}{7}.\dfrac{4}{35}+\dfrac{12}{7}.\dfrac{\left(-31\right)}{35}-\dfrac{2}{7}\)
b) \(1+2-3-4+5+5-7-8+...+97+98-99-100\)
c) \(A=157.\left(-37\right)-\left(41.53-37.157\right)+51.53\)
d) \(B=\left(\dfrac{1}{11}+\dfrac{1}{21}+\dfrac{1}{31}+\dfrac{1}{41}+\dfrac{1}{51}\right)\left(\dfrac{-41}{123}+\dfrac{31}{-186}-\dfrac{-51}{102}\right)\)
Câu 2 :
a) 12 ( x - 5 ) = 7x - 5
b) Tìm x \(\in\) Z sao cho : ( 2x - 3 ) 2010 = ( 2x - 3 ) 2012
Câu 3 :
1) Cho biểu thức S = 1 + 3 + 32 + 33 +...+ 3202 + 3 203
a) chứng tỏ rằng tổng S chia hết cho 52 .
b) Tìm Chữ số tận cùng trong tổng S .
2 ) Cho biểu thức A= \(\dfrac{2n+1}{2n+5}\) . Chứng tỏ rằng với mọi số tự nhiên n thì A là phân số tối giản .
Câu 4 : So sánh tổng gồm 1006 số hạng :
\(S=\dfrac{1}{1.1.3}+\dfrac{1}{2.3.5}+\dfrac{1}{3.5.7}+...+\dfrac{1}{1006.2011.2013}\) với \(\dfrac{2}{3}\)
Tính :
\(A=\dfrac{101+100+99+98+...+3+2+1}{101-100+99-98+...+3-2+1}\)
Bài 1:
a,|x-3|+|2-x|0
b,left(2-dfrac{3}{4}xright).left(x+1right)0
bài 2:
a,Adfrac{dfrac{-6}{7}+dfrac{6}{13}-dfrac{6}{29}}{dfrac{9}{7}-dfrac{9}{13}+dfrac{9}{29}}
b,Bdfrac{dfrac{2}{15}-dfrac{2}{21}+dfrac{2}{39}}{0,25-dfrac{5}{28}+dfrac{5}{52}}
c,Cdfrac{50-dfrac{4}{15}+dfrac{2}{15}-dfrac{2}{17}}{100-dfrac{8}{13}+dfrac{4}{15}-dfrac{4}{17}}:dfrac{1+dfrac{2}{21}-dfrac{5}{121}}{dfrac{65}{121}-dfrac{26}{71}-13}
Đọc tiếp
Bài 1:
a,\(|x-3|+|2-x|=0\)
b,\(\left(2-\dfrac{3}{4}x\right).\left(x+1\right)=0\)
bài 2:
a,A=\(\dfrac{\dfrac{-6}{7}+\dfrac{6}{13}-\dfrac{6}{29}}{\dfrac{9}{7}-\dfrac{9}{13}+\dfrac{9}{29}}\)
b,B=\(\dfrac{\dfrac{2}{15}-\dfrac{2}{21}+\dfrac{2}{39}}{0,25-\dfrac{5}{28}+\dfrac{5}{52}}\)
c,C=\(\dfrac{50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}}{100-\dfrac{8}{13}+\dfrac{4}{15}-\dfrac{4}{17}}:\dfrac{1+\dfrac{2}{21}-\dfrac{5}{121}}{\dfrac{65}{121}-\dfrac{26}{71}-13}\)
Cho A=\(\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{11}+\dfrac{1}{15}+\dfrac{1}{19}+...+\dfrac{1}{99}\)
Tính A.
19 tháng 2 2021 lúc 20:46
[ 1+2dfrac{1}{3}-3dfrac{1}{4}]:[1+3dfrac{7}{12}-4dfrac{1}{2}] tính
Đọc tiếp
[ 1+2\(\dfrac{1}{3}\)-3\(\dfrac{1}{4}\)]:[1+3\(\dfrac{7}{12}\)-4\(\dfrac{1}{2}\)]
tính
Tính ( bằng cách thuận tiên nếu có thể )
a, A dfrac{3^2}{10}+dfrac{3^2}{40}+dfrac{3^2}{8^8}+...+dfrac{3^2}{340}
b, A dfrac{5^2}{1cdot6}+dfrac{5^2}{6cdot11}+...+dfrac{5^2}{26cdot31}
c, A dfrac{1}{2}+dfrac{2}{2cdot4}+dfrac{3}{4cdot7}+dfrac{4}{7cdot11}+dfrac{5}{11cdot16}
d, A dfrac{3}{54}+dfrac{5}{126}+dfrac{7}{249}+dfrac{8}{609}
e, A dfrac{2}{3}+dfrac{14}{15}+dfrac{34}{35}+dfrac{62}{63}
Đọc tiếp
Tính ( bằng cách thuận tiên nếu có thể )
a, A = \(\dfrac{3^2}{10}\)+\(\dfrac{3^2}{40}\)+\(\dfrac{3^2}{8^8}\)+...+\(\dfrac{3^2}{340}\)
b, A = \(\dfrac{5^2}{1\cdot6}\)+\(\dfrac{5^2}{6\cdot11}\)+...+\(\dfrac{5^2}{26\cdot31}\)
c, A = \(\dfrac{1}{2}\)+\(\dfrac{2}{2\cdot4}\)+\(\dfrac{3}{4\cdot7}\)+\(\dfrac{4}{7\cdot11}\)+\(\dfrac{5}{11\cdot16}\)
d, A = \(\dfrac{3}{54}+\dfrac{5}{126}+\dfrac{7}{249}+\dfrac{8}{609}\)
e, A = \(\dfrac{2}{3}+\dfrac{14}{15}+\dfrac{34}{35}+\dfrac{62}{63}\)
1) Tìm x biết:
\(\left(1-\dfrac{3}{10}-x\right):\left(\dfrac{19}{10}-1-\dfrac{2}{5}\right)+\dfrac{4}{5}=1\)
2) Tính nhanh
a)\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{10.11.12}\)
b)\(\dfrac{1^2}{1.2}.\dfrac{2^2}{2.3}.\dfrac{3^2}{3.4}.\dfrac{4^2}{4.5}\)
1.
a, ^{^2}left(x-2right)9 b,^{^3}left(3x-1right)-8 c, left(x+dfrac{1}{2}right)^2dfrac{1}{16} d, left(dfrac{2}{3}right)^xdfrac{4}{9} e, left(dfrac{1}{2}right)^{x-1}dfrac{1}{16} f,left(dfrac{1}{2}right)^{2x-1}8
2.tìm số tự nhiên n biết
a, 3^{n-1}27 b, 3^{n-1}dfrac{1}{243} c, left(dfrac{1}{2}right)^{2n-1}dfrac{1}{8} d, left(-dfrac{1}{3}right)^{n-5}dfrac{1}{81} e,2^{-1}.2^n+4.2^n9.2^5
Đọc tiếp
1.
a, \(^{^2}\left(x-2\right)=9\) b,\(^{^3}\left(3x-1\right)=-8\) c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\) d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\) e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\) f,\(\left(\dfrac{1}{2}\right)^{2x-1}=8\)
2.tìm số tự nhiên n biết
a, \(3^{n-1}=27\) b, \(3^{n-1}=\dfrac{1}{243}\) c, \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\) d, \(\left(-\dfrac{1}{3}\right)^{n-5}=\dfrac{1}{81}\) e,\(2^{-1}.2^n+4.2^n=9.2^5\)