Tính
4x5x6/12x15x9
6x8x11/33x16
giúp mình với
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\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{6.7.8}\)
\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{6.7}-\frac{1}{7.8}\)
\(=\frac{1}{1.2}-\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{56}\)
\(=\frac{28}{56}-\frac{1}{56}=\frac{27}{56}\)
Dấu . là nhân nha
\(\frac{2}{1.2.3}=\frac{1}{1.2}-\frac{1}{2.3}\)
\(\frac{2}{2.3.4}=\frac{1}{2.3}-\frac{1}{3.4}\)
.......................................
\(\frac{2}{6.7.8}=\frac{1}{6.7}-\frac{1}{7.8}\)
S= \(\frac{1}{1.2}-\frac{1}{7.8}=\frac{27}{56}\)
ta có : B = 1.2.3 + 2.3.4 + 3.4.5 + ...... + 2016.2017.2018
4B = 1.2.3.4 - 1.2.3.4 + 2.3.4.5 - 2.3.4.5 + ...... + 2016.2017.2018.2019
4B = 2016.2017.2018.2019
vậy B = 2016.2017.2018.2019/4
Ta có : B = 1.2.3 + 2.3.4 + ...... + 2016.2017.2018
=> 4B = 1.2.3.4 - 1.2.3.4 + 2.3.4.5 - 2.3.4.5 + ...... + 2016.2017.2018.2019
=> 4B = 2016.2017.2018.2019
=> B = 2016.2017.2018.2019/4
`(4xx5xx6)/(12xx8xx10)=(4xx5xx6)/(6xx2xx4xx2xx5xx2)= 1/(2xx2xx2)=1/8`
5*6*7*9/12*7*27
=5*6*7*3*2/2*6*7*3*3
=5*1*1*1*1/1*1*1*1*3
=5/3
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
Ta có:
\(A=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Leftrightarrow3A=99.100.101\Leftrightarrow A=\frac{99.100.101}{3}=333300\)
\(B=1.2.3+2.3.4+4.5.6+...+98.99.100\)
\(\Rightarrow4B=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+4.5.6.\left(7-3\right)+...+98.99.100.\left(101-97\right)\)
\(\Rightarrow4B=1.2.3.4+2.3.4.5-1.2.3.4+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100\)
\(\Leftrightarrow4B=98.99.100.101\Leftrightarrow B=\frac{98.99.100.101}{4}=24497550\)
\(\frac{4\times5\times6}{12\times15\times9}\)\(=\frac{2\times2\times5\times6}{2\times6\times3\times5\times9}\)\(=\frac{2}{3\times9}\)\(=\frac{2}{27}\)
\(\frac{6\times8\times11}{33\times16}\)\(=\frac{2\times3\times8\times11}{3\times11\times8\times2}\)\(=\)\(1\)
~ HOK TỐT ~
4×5×612×15×912×15×94×5×6=2×2×5×62×6×3×5×9=2×6×3×5×92×2×5×6=23×9=3×92=227=272
6×8×1133×1633×166×8×11=2×3×8×113×11×8×2=3×11×8×22×3×8×11==11