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\(D=\dfrac{5}{1\cdot2}+...+\dfrac{5}{199\cdot200}\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{199}{200}=\dfrac{199}{80}\)
Lời giải:
\(D=5\times \left(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{199\times 200}\right)\)
\(=5\times \left(\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+...+\frac{200-199}{199\times 200}\right)\)
\(=5\times \left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}\right)=5\times (1-\frac{1}{200})\)
\(=5\times \frac{199}{200}=\frac{995}{200}=\frac{199}{40}\)
\(E=\dfrac{0.5}{1.2}+\dfrac{0.5}{2\cdot3}+...+\dfrac{0.5}{199\cdot200}\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{200}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{199}{200}=\dfrac{199}{400}\)
#)Giải :
a) \(\frac{2xX-4,36}{0,125}=\)0,25 x 42,9 - 11,7 x 0,25 + 0,25 x 0,8
\(\frac{2xX-4,36}{0,125}=\)0,25 x ( 42,9 - 11,7 + 0,8 )
\(\frac{2xX-4,36}{0,125}=\)0,25 x 32
\(\frac{2xX-4,36}{0,125}=8\)
\(2xX-4,36=8x0,125\)
\(2xX-4,36=1\)
\(2xX=1+4,36\)
\(2xX=5,36\)
\(X=5,36:2\)
\(X=2,68\)
#~Will~be~Pens~#
\(N=\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+...+\frac{1}{2005.2010}\)
\(N=\frac{1}{5}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{2005}-\frac{1}{2010}\right)\)
\(N=\frac{1}{5}.\left(1-\frac{1}{2010}\right)\)
\(N=\frac{1}{5}.\frac{2009}{2010}\)
\(N=\frac{2009}{10050}\)
Lời giải:
Gọi phân số trên là $A$. Ta có:
$A=\frac{12,48:6,48\times 2\times 8\times 6,25\times 3,25\times 4\times 4\times 2}{3,12\times 21,6\times 1,25\times 2,6\times 4\times 4\times 10\times 10}$
$=\frac{12,48:6,48\times (2\times 6,25)\times (8\times 3,25)\times 2}{3,12\times 21,6\times (1,25\times 10)\times (2,6\times 10)}$
$=\frac{12,48:6,48\times 12,5\times 26\times 2}{3,12\times 21,6\times 12,5\times 26}$
$=\frac{12,48:6,48\times 2}{3,12\times 21,6}=\frac{125}{2187}$
0,25 cái gì = giờ bạn
0,25 cái gì = giờ bạn
0,25 cái gì = giờ bạn
0,25 cái gì = giờ bạn
\(H=0,25\times\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{19\times20}\right)\)
\(=0,25\times\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=0,25\times\left(1-\dfrac{1}{20}\right)=0,25\times\dfrac{19}{20}=\dfrac{19}{80}\)
\(H=\dfrac{0.25}{1\cdot2}+\dfrac{0.25}{2\cdot3}+...+\dfrac{0.25}{199\cdot200}\)
\(=\dfrac{1}{4}\cdot\dfrac{199}{200}=\dfrac{199}{800}\)