câu 1: cmr
A=1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ....+ 1/50^2
chứng minh a bé hơn 2
câu 2 : tính tổng
S = 3 + 3/2 + 3/2^2 + ....+3/2^9
câu 3 : Ss 1/2.3 với 1/2 - 1/3
câu 4 : thực hiện phép tính
M = 9/40 - 11/60 + 13/84 - 15/112
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Những câu hỏi liên quan
3 tháng 6 2021
Giải:
a) \(\left(9\dfrac{4}{9}+5\dfrac{2}{3}\right)-5\dfrac{1}{2}\)
\(=\left(\dfrac{85}{9}+\dfrac{17}{3}\right)-\dfrac{11}{2}\)
\(=\dfrac{136}{9}-\dfrac{11}{2}\)
\(=\dfrac{173}{18}\)
b) \(\dfrac{13}{9}.\dfrac{15}{4}-\dfrac{13}{9}.\dfrac{7}{4}-\dfrac{13}{9}.\dfrac{5}{4}\)
\(=\dfrac{13}{9}.\left(\dfrac{15}{4}-\dfrac{7}{4}-\dfrac{5}{4}\right)\)
\(=\dfrac{13}{9}.\dfrac{3}{4}\)
\(=\dfrac{13}{12}\)
c) \(\dfrac{2}{3}+\dfrac{5}{8}-\dfrac{-1}{3}+0,375\)
\(=\left(\dfrac{2}{3}-\dfrac{-1}{3}\right)+\left(\dfrac{5}{8}+\dfrac{3}{8}\right)\)
\(=1+1\)
\(=2\)
d) \(75\%-3\dfrac{1}{2}+1,5:\dfrac{10}{7}\)
\(=\dfrac{3}{4}+\dfrac{7}{2}+\dfrac{3}{2}:\dfrac{10}{7}\)
\(=\dfrac{3}{4}+\dfrac{7}{2}+\dfrac{21}{20}\)
\(=\dfrac{53}{10}\)
e) \(1\dfrac{13}{15}.\left(0,5\right)^2.3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
\(=\dfrac{28}{15}.\dfrac{1}{4}.3+\left(\dfrac{8}{15}-\dfrac{79}{60}\right):\dfrac{47}{24}\)
\(=\dfrac{7}{5}+\dfrac{-47}{60}:\dfrac{47}{24}\)
\(=\dfrac{7}{5}+\dfrac{-2}{5}\)
\(=1\)
23 tháng 9 2021
d: \(\dfrac{1}{27}:\left(-\dfrac{1}{3}\right)^2+75\%\cdot\left(-\dfrac{2^2}{3}\right)\)
\(=\dfrac{1}{27}:\dfrac{1}{9}+\dfrac{3}{4}\cdot\dfrac{-4}{3}\)
\(=\dfrac{1}{3}-1\)
\(=-\dfrac{2}{3}\)
TN
6 tháng 8 2016
1)
a. \(\left(3x^2-50\right)^2=5^4\)
\(\Leftrightarrow3x^4-50=625\)
\(\Leftrightarrow3x^4=675\)
\(\Leftrightarrow x^4=225\)
\(\Leftrightarrow x=\sqrt{15}\)
2)
a. \(\frac{\left(3^4-3^3\right)^4}{27^3}=\frac{3^{16}-3^{12}}{\left(3^3\right)^3}=\frac{3^{12}.3^4-3^{12}}{3^9}=\frac{3^{12}\left(3^4-1\right)}{3^9}\)
\(=\frac{3^{12}.80}{3^9}=3^3.80=27.80=2160\)
b. \(\frac{25^3}{\left(5^5-5^3\right)^2}=\frac{\left(5^2\right)^3}{5^{10}-5^6}=\frac{5^6}{5^6.5^4-5^6}=\frac{5^6}{5^6\left(5^4-1\right)}\)
\(=\frac{5^6}{5^6.624}=\frac{1}{624}\)
25 tháng 6 2023
4:
a: =4/15-2,9+11/15=1-2,9=-1,9
b: \(=-36,75+3,7-63,25+6,3=10-100=-90\)
c: \(=6,5+3,5-\dfrac{10}{17}-\dfrac{7}{17}=10-1=9\)
d: \(=\dfrac{13}{25}\left(-39,1-60,9\right)=\dfrac{13}{25}\left(-100\right)=-52\)
e: =-5/12-7/12-3,7-6,3=-1-10=-11
f: =2,8(-6/13-7/13)-7,2=-2,8-7,2=-10
25 tháng 6 2023
`@` `\text {Ans}`
`\downarrow`
`a.`
`A=(1/2-7/13-1/3)+(-6/13+1/2+1 1/3)`
`= 1/2 - 7/13 - 1/3 - 6/13 + 1/2 + 1 1/3`
`= (1/2 + 1/2) + (-7/13 - 6/13) + (-1/3 + 1 1/3) `
`= 1 - 1 + 1`
`= 1`
`b.`
`B=0,75+2/5+(1/9-1 1/2+5/4)`
`= 3/4 + 2/5 + 1/9 - 3/2 + 5/4`
`= (3/4+5/4)+ 1/9 + 2/5 - 3/2`
`= 2 + 1/9 - 11/10`
`= 19/9 - 11/10`
`= 91/90`
`c.`
`(-5/9).3/11+(-13/18).3/11`
`= 3/11*[(-5/9) + (-13/18)]`
`= 3/11*(-23/18)`
`= -23/66`
`d.`
`(-2/3).3/11+(-16/9).3/11`
`= 3/11* [(-2/3) + (-16/9)]`
`= 3/11*(-22/9)`
`= -2/3`
`e.`
`(-1/4).(-2/13)-7/24.(-2/13)`
`= (-2/13)*(-1/4-7/24)`
`= (-2/13)*(-13/24)`
`= 1/12`
`f.`
`(-1/27).3/7+(5/9).(-3/7)`
`= 3/7*(-1/27 - 5/9)`
`= 3/7*(-16/27)`
`= -16/63`
`g.`
`(-1/5+3/7):2/11+(-4/5+4/7):2/11`
`=[(-1/5+3/7)+(-4/5+4/7)] \div 2/11`
`= (-1/5+3/7 - 4/5 + 4/7) \div 2/11`
`= [(-1/5-4/5)+(3/7+4/7)] \div 2/11`
`= (-1+1) \div 2/11`
`= 0 \div 2/11 = 0`
TT
1
19 tháng 11 2023
Từ 1 đến 2002 sẽ có:
\(\left(2002-1\right):1+1=2002\left(số\right)\)
=>Sẽ có 2002/2=1001 cặp có tổng là -1 là (1;-2);(3;-4);...;(2001;-2002)
M=1+(-2)+3+(-4)+...+2001+(-2002)+2003
=(1-2)+(3-4)+...+(2001-2002)+2003
=2003-1*1001
=2003-1001
=1002
26 tháng 6 2023
15: A= 1/3-3/4+3/5+1/2007-1/36+1/15-2/9
Sửa đề:
A=-3/4-2/9-1/36+1/3+3/5+1/15+1/2007
=-27/36-8/36-1/36+5/15+9/15+1/15+1/2007
=-1+1+1/2007=1/2007
16:
\(A=\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}\)
=1/64
17:
=1/2-1/2+2/3-2/3+3/4-3/4+4/5-4/5+5/6-5/6-6/7
=-6/7
Câu 1:
\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.....+\frac{1}{50^2}\)
\(A=\frac{1}{1\times1}+\frac{1}{2\times2}+\frac{1}{3\times3}+\frac{1}{4\times4}+.....+\frac{1}{50\times50}\)
\(A< \frac{1}{1\times1}+\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+.....+\frac{1}{49\times50}\)
\(A< 1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{49}-\frac{1}{50}\)
\(A< 2-\frac{1}{50}< 2\)
Câu 2:
\(S=3+\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^9}\)
\(2S=6+3+\frac{3}{2}+.....+\frac{3}{2^8}\)
\(2S-S=\left(6+3+\frac{3}{2}+.....+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
\(S=\frac{3069}{512}\)
Câu 3:
\(\frac{1}{2\times3}=\frac{1}{6}\)
\(\frac{1}{2}-\frac{1}{3}=\frac{3}{6}-\frac{2}{6}=\frac{1}{6}\)
\(\Rightarrow\frac{1}{2\times3}=\frac{1}{2}-\frac{1}{3}\)
Câu 4:
\(M=\frac{9}{40}-\frac{11}{60}+\frac{13}{84}-\frac{15}{112}\)
\(M=\left(\frac{9}{40}-\frac{11}{60}\right)+\left(\frac{13}{84}-\frac{15}{112}\right)\)
\(M=\left(\frac{27}{120}-\frac{22}{120}\right)+\left(\frac{52}{336}-\frac{45}{336}\right)\)
\(M=\frac{1}{24}+\frac{1}{48}\)
\(M=\frac{2+1}{48}\)
\(M=\frac{3}{48}\)
\(M=\frac{1}{16}\)
Chúc bạn học tốt
câu 2:
s= 3+3/2+3/3^2+.....+3/2^9
=> 2s=6+3+3/2+...+3/2^8
=> 2s-s =( 6+3+3/2 + ....+3/2^8)- ( 3+3/2 +3/2^2+...+3/2^9)
=> s=6-3/2^9=3069/512