Tính nhanh :
\(\text{A}=\left(1\times2\right)^{-1}+(2\times3)^{-1}+(3\times4)^{-1}+...+\left(9\times10\right)^{-1}\)
Những câu hỏi liên quan
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{5\times6}\right)\times10-x=0\)
Ta thấy :
1/1x2 = 1/1 - 1/2
1/2x3 = 1/2 - 1/3
....
=>( 1/1x2 + 1/2x3 + 1/3x4 + 1/5x6 ) x 10 - x = ( 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 ) x 10 - x
= ( 1/1 - 1/6 ) x 10 - x =0
5/6 x 10 - x = 0
25/3 - x = 0
=> x = 25/3
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\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{5.6}\right).10-x=0\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{30}\right).10-x=0\)
\(\left(1-\frac{1}{4}+\frac{1}{30}\right).10-x=0\)
\(\left(\frac{3}{4}+\frac{1}{30}\right).10-x=0\)
\(\frac{47}{60}.10-x=0\)
\(\frac{47}{6}-x=0\)
\(x=\frac{47}{6}-0\)
\(x=\frac{47}{6}\)
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Xem thêm câu trả lời
Tính nhanh :
A = \(\frac{1,25\times10\div0,25\times24,4\times2}{6,1\times2\times6,25\times4\div0,5}+\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right).........\left(1-\frac{1}{19}\right)\times\left(1-\frac{1}{20}\right)\)
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Link: https://h.vn/hoi-dap/question/633709.html
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\(A=\frac{1.25.10:0,25.24,4.2}{6,1.2.6,25.4:0,5}.\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{19}\right).\left(1-\frac{1}{20}\right)\)
\(A=\frac{50.48,8}{6,1.100}\times\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{18}{19}\times\frac{19}{20}\)
\(A=\frac{4}{1}\times\frac{1}{1}\times\frac{1}{20}\)
\(A=\frac{4}{20}\)
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Tìm x biết \(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\right)\times10-x=0\)
( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +1/5.6 ) x 10 - x = 0
= ( 1- 1/2 +1/2 -1/3 +1/3 - 1/4 + 1/4 - 1/5 +1/5 -1/6 ) x 10 - x = 0
= ( 1 - 1/6 ) x 10 - x = 0
= 5/6 x 10 - x =0
= 25/3 - x =0
x = 25/3 - 0
x = 25/3
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\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{6}\right)\times10-x=0\)
\(\frac{5}{6}\times10-x=0\)
\(\frac{25}{3}-x=0\)
x =\(\frac{25}{3}-0=\frac{25}{3}\)
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Tính nhanh : \(\frac{1}{8}\div12,5\%+\left(\frac{1\times2\times3+6\times4\times2}{5\times3\times1+5\times15\times25}+\frac{1}{2}\div50\%\right)-\left(\frac{1}{16}\div6,25\%+\frac{3+2+1+2+4+6}{1+3+5+25+15+5}\right)-\frac{1}{4}\div25\%\)
\(\frac{1}{8}=12,5\%\) ; \(\frac{1}{16}=6,25\%\) ; \(\frac{1}{2}=50\%\) ; \(\frac{1}{4}=25\%\)
Thay vào trên mà tính.
= \(1+\left(\frac{3\left(1x2+2x4x2\right)}{3\left(5+5x3x25\right)}+1\right)-\left(1+\frac{18}{54}\right)-1\) = \(\frac{18}{380}-\frac{18}{54}\)
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Thực hiện phép tính:a)1times2times3times......times9-1times2times3times......times8-1times2times3times.....times8times8b)Bfrac{left(3times4times2^{16}right)^2}{11times2^{13}times4^{11}-16^9}c)C70timesleft(frac{131313}{565656}+frac{131313}{727272}+frac{131313}{909090}right)d)Bfrac{1}{4times9}+frac{1}{9times14}+frac{1}{14times19}+...+frac{1}{64times69}GIÚP MIK VỚI AI NHANH MIK CHO 3 TICK LUÔN CHO NHA!!!!!!!!!!NHỚ TRÌNH BÀY RÕ RÀNG NHA!!!!!!HELP ME
Đọc tiếp
Thực hiện phép tính:
a)\(1\times2\times3\times......\times9-1\times2\times3\times......\times8-1\times2\times3\times.....\times8\times8\)
b)\(B=\frac{\left(3\times4\times2^{16}\right)^2}{11\times2^{13}\times4^{11}-16^9}\)
c)\(C=70\times\left(\frac{131313}{565656}+\frac{131313}{727272}+\frac{131313}{909090}\right)\)
d)\(B=\frac{1}{4\times9}+\frac{1}{9\times14}+\frac{1}{14\times19}+...+\frac{1}{64\times69}\)
GIÚP MIK VỚI AI NHANH MIK CHO 3 TICK LUÔN CHO NHA!!!!!!!!!!NHỚ TRÌNH BÀY RÕ RÀNG NHA!!!!!!HELP ME
a)1.2.3.4...9-1.2.3.4...8-1.2.3.4...8.8
=1.2.3.4...8(9-1-8)
=1.2.3.4...8.0
=0
b)(3.4.216)2/11.123.411-169=(3.22.216)2/11.213.222-236=32.24.232/11.235-236=32.226/235.(11-2)
=32.236/235.9=32.236/235.32=2
c)70.(131313/565656+131313/727272+131313/909090
=70.(13/56+13/72+13/90)
=70.39/70=39
d)1/4.9+1/9.14+1/14.19+...+1/64.69
=4/4.9.4+4/9.4.14+4/14.19.4+...+4/64.69.4.
=1/4.(4/4.9+4/9.14+4/14.19+...+4/64.69)
=1/4.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)
=1/4.(1/4-1/69)
=1/4.65/276=65/1104
~~~~~~~~Chúc bạn học giỏi nhé !~~~~~~~~
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d)\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\right)\)
\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{69}\right)\)
\(\frac{1}{3}\times\frac{65}{276}\)
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Xem thêm câu trả lời
Cho B= \(\frac{1\times2}{1\times2\times3}+\frac{1\times2}{1\times2\times4}+\frac{1\times2}{1\times2\times3\times4}+\frac{1\times2}{1\times2\times3\times4\times5}+....+\frac{1\times2}{n,giao}\left(n\in N,n\ge3\right)\)
chứng tỏ B nhỏ hơn 3
\(\dfrac{4^{10}\times9^6+3^{12}\times8^5}{6^{13}\times4-2^{16}\times3^{12}}\)
\(\dfrac{2^4\times2^6}{\left(2^5\right)^2}-\dfrac{2^5\times15^3}{6^3\times10^2}\)
\(\dfrac{\left(-2\right)^{10}\times3^{31}+2^{40}\times\left(-3\right)^6}{\left(-2\right)^{11}\times\left(-3\right)^{31}+2^{41}\times3^6}\)
giải chi tiết giúp mình nhé
\(A=\left[1-\left(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+......+\frac{1}{98\times99\times100}\right)\right]\times\frac{14851}{19800}\)
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{9\times10}\right)\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
tìm X
<=> (1-1/10)(x-1)+x/10=x-9/10
<=> 9x/10-9/10+x/10=x-9/10
<=> x=x
Như vậy, phương trình thỏa mãn với mọi x
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