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Đặt P = ... ( biểu thức đề bài )
Nhận xét: Với \(k\inℕ^∗\) ta có:
\(\frac{k+2}{k!+\left(k+1\right)!+\left(k+2\right)!}=\frac{k+2}{k!+\left(k+1\right).k!+\left(k+2\right).k!}=\frac{k+2}{2.k!\left(k+2\right)}=\frac{1}{2.k!}\)
\(\Rightarrow\)\(P=\frac{1}{2.1!}+\frac{1}{2.2!}+...+\frac{1}{2.6!}=\frac{1}{2}\left(1+\frac{1}{2}+...+\frac{1}{720}\right)=...\)
\(\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\div\dfrac{1}{7}\)
\(=\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\times\dfrac{7}{1}\)
\(=\dfrac{3\times4\times5\times6\times7}{4\times5\times6\times7\times1}\)
\(=\dfrac{3}{1}=3\)
`1/7+5/6+4/7+3/6+2/7+4/6`
`=(1/7 + 4/7 + 2/7 )+(5/6 + 3/6 +4/6)`
`= 7/7 + 12/6`
`=1+2`
`=3`
`1/7+5/6+4/7+3/6+2/7+4/6`
`=(1/7+4/7+2/7)+(5/6+3/6+4/6)`
`=7/7+12/6`
`=1+2`
`=3`
= (1/7+7/1)+(2/6+6/2)+(3/5+5/3)+4/4
= 7/1/7+3/1/3+2/4/15+1
= 13/26/35
= 51/20
----------------------------------
= 3/14
------------------------------------
= 4/7 - 2/7
= 2/7
--------------------------------------
= 17/45
---------------------------------------
= 2/3
--------------------------------------
= 2 x 1/4
= 1/2
2+3+4+5+8+7+6+5+1+2+3+4+9+8+7+6+2+4+8+6.
= 100
Chúc bạn học tốt !
^^
= \(\frac{1}{2}\)- \(\frac{2}{3}\)+ (\(\frac{3}{4}\)- \(\frac{3}{4}\)) + ( -\(\frac{4}{5}\)+ \(\frac{4}{5}\)) + ( \(\frac{5}{6}-\frac{5}{6}\)) - \(\frac{6}{7}\)
= \(\frac{1}{2}-\frac{2}{3}-0-0-0-\frac{6}{7}\)
= \(\frac{1}{2}-\frac{2}{3}-\frac{6}{7}\)
=\(\frac{21}{42}-\frac{28}{42}-\frac{36}{42}\)
= \(\frac{-43}{42}\)