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\(1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{200}\left(1+2+...+200\right)\)
Thực hiện phép tính:1, left(dfrac{-1}{2}right)^2.left|+8right|-left(-dfrac{1}{2}right)^3:left|-dfrac{1}{16}right|2, left|-0,25right|-left(-dfrac{3}{2}right)^2:dfrac{1}{4}+dfrac{3}{4}.2017^03, left|dfrac{2}{3}-dfrac{5}{6}right|.left(3,6:2dfrac{2}{5}right)^34, left|left(-0,5right)^2+dfrac{7}{2}right|.10-left(dfrac{29}{30}-dfrac{7}{15}right):left(-dfrac{2017}{2018}right)^05, dfrac{8}{3}+left(3-dfrac{1}{2}right)^2-left|dfrac{-7}{3}right|
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Thực hiện phép tính:
1, \(\left(\dfrac{-1}{2}\right)^2.\left|+8\right|-\left(-\dfrac{1}{2}\right)^3:\left|-\dfrac{1}{16}\right|\)
2, \(\left|-0,25\right|-\left(-\dfrac{3}{2}\right)^2:\dfrac{1}{4}+\dfrac{3}{4}.2017^0\)
3, \(\left|\dfrac{2}{3}-\dfrac{5}{6}\right|.\left(3,6:2\dfrac{2}{5}\right)^3\)
4, \(\left|\left(-0,5\right)^2+\dfrac{7}{2}\right|.10-\left(\dfrac{29}{30}-\dfrac{7}{15}\right):\left(-\dfrac{2017}{2018}\right)^0\)
5, \(\dfrac{8}{3}+\left(3-\dfrac{1}{2}\right)^2-\left|\dfrac{-7}{3}\right|\)
1) Tính tổng C left(1-dfrac{1}{2}right).left(1-dfrac{1}{3}right).left(1-dfrac{1}{4}right).....left(1-dfrac{1}{2022}right)
2) Cho tổng A dfrac{1}{3} - dfrac{2}{3^2} + dfrac{3}{3^3} - dfrac{4}{3^4} +...+ dfrac{99}{3^{99}} - dfrac{100}{3^{100}}. Chứng tỏ rằng A dfrac{3}{16}
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1) Tính tổng C = \(\left(1-\dfrac{1}{2}\right)\).\(\left(1-\dfrac{1}{3}\right)\).\(\left(1-\dfrac{1}{4}\right)\).....\(\left(1-\dfrac{1}{2022}\right)\)
2) Cho tổng A = \(\dfrac{1}{3}\) - \(\dfrac{2}{3^2}\) + \(\dfrac{3}{3^3}\) - \(\dfrac{4}{3^4}\) +...+ \(\dfrac{99}{3^{99}}\) - \(\dfrac{100}{3^{100}}\). Chứng tỏ rằng A < \(\dfrac{3}{16}\)
Chứng tỏ rằng:\(P=\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{2^2}\right).\left(1+\dfrac{1}{2^3}\right).....\left(1+\dfrac{1}{2^{200}}\right)< 3\)
\(A=\left(1-\dfrac{1}{2^2}\right).\left(1-\dfrac{1}{3^2}\right).\left(1-\dfrac{1}{4^2}\right)....\left(1-\dfrac{1}{30^2}\right)\)
Cho A=\(\left(\dfrac{1}{2^2}-1\right)\)\(\left(\dfrac{1}{3^2}-1\right)\)\(\left(\dfrac{1}{4^2}-1\right)\)...\(\left(\dfrac{1}{2013^2}-1\right)\)\(\left(\dfrac{1}{2014^2}-1\right)\) và B= \(-\dfrac{1}{2}\)
Hãy so sánh A và B
28 tháng 1 2022 lúc 21:48
Tính giá trị biểu thức:e,dfrac{18}{37}+dfrac{8}{24}+dfrac{19}{37}-1dfrac{23}{24}+dfrac{2}{3}f,left(-2right)^3.left(dfrac{3}{4}-0,25right):left(2dfrac{1}{4}-1dfrac{1}{6}right)g,left(dfrac{2}{5}right)^2+5dfrac{1}{2}.left(4,5-2right)+dfrac{2^3}{left(-4right)}h,dfrac{4}{9}.19dfrac{1}{3}-dfrac{4}{9}.39dfrac{1}{3}i,left(-dfrac{1}{2}right)^2:dfrac{1}{4}-2left(-dfrac{1}{2}right)^2j,125%.left(dfrac{-1}{2}right)^2:left(1dfrac{5}{16}-1,5right)+2008^0k,left(-2right)^3.dfrac{-1}{24}+left(dfrac{4}{3}-1dfrac{5...
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Tính giá trị biểu thức:
\(e,\dfrac{18}{37}+\dfrac{8}{24}+\dfrac{19}{37}-1\dfrac{23}{24}+\dfrac{2}{3}\)
\(f,\left(-2\right)^3.\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)
\(g,\left(\dfrac{2}{5}\right)^2+5\dfrac{1}{2}.\left(4,5-2\right)+\dfrac{2^3}{\left(-4\right)}\)
\(h,\dfrac{4}{9}.19\dfrac{1}{3}-\dfrac{4}{9}.39\dfrac{1}{3}\)
\(i,\left(-\dfrac{1}{2}\right)^2:\dfrac{1}{4}-2\left(-\dfrac{1}{2}\right)^2\)
\(j,125\%.\left(\dfrac{-1}{2}\right)^2:\left(1\dfrac{5}{16}-1,5\right)+2008^0\)
\(k,\left(-2\right)^3.\dfrac{-1}{24}+\left(\dfrac{4}{3}-1\dfrac{5}{6}\right):\dfrac{5}{12}\)
Tính giá trị biểu thức sau:
\(D=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\)
A-5^{22}-left{-222-left[-122-left(100-5^{22}right)+2022right]right}
B1+dfrac{1}{2}left(1+2right)+dfrac{1}{3}left(1+2+3right)+...+dfrac{1}{20}left(1+2+3+...+20right)
Cdfrac{5.4^6.9^4-3^9.left(-8right)^4}{4.2^{13}.3^8+2.8^4.left(-27right)^3}
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\(A=-5^{22}-\left\{-222-\left[-122-\left(100-5^{22}\right)+2022\right]\right\}\)
\(B=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{20}\left(1+2+3+...+20\right)\)
\(C=\dfrac{5.4^6.9^4-3^9.\left(-8\right)^4}{4.2^{13}.3^8+2.8^4.\left(-27\right)^3}\)