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\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100} \)
\(=\frac{1}{3}.\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)=\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)=\frac{1}{18}-\frac{1}{6.970200}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100}\)
=\(\frac{1}{3}\cdot\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{4.5.6}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)\)
=\(\frac{1}{18}-\frac{1}{5821200}\)
1+2(25+9)−43=1+2⋅34−64=
nhưng lam gì có phép nhân ở 1+2(25 + 9 )
(-25)-(-12)= - 13
18+(14-42)=18+(-28) = -10
(-18)-13+17=(-31) +17= -14
\(\rightarrow\)-13 < -10 > -14\(\Rightarrow\) (-25)-(-12) < 18+(14-42) > (-18)-13+17
Thay y = -24 ta có :
-90 - (-24 + 10 ) +100
= -90 + 14 + 100
= 24
Ta có : \(A=\dfrac{1}{199}-\dfrac{1}{199.198}-\dfrac{1}{198.197}-\dfrac{1}{197.196}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
\(=\dfrac{1}{199}-\left(\dfrac{1}{199.198}+\dfrac{1}{198.197}+\dfrac{1}{197.196}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)
\(=\dfrac{1}{199}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{196.197}+\dfrac{1}{197.198}+\dfrac{1}{198.199}\right)\)
\(=\dfrac{1}{199}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...-\dfrac{1}{198}+\dfrac{1}{198}-\dfrac{1}{199}\right)\)
\(=\dfrac{1}{199}-\left(1-\dfrac{1}{199}\right)\)
\(=\dfrac{1}{199}-\dfrac{198}{199}=\dfrac{-197}{199}\)
~ Học tốt ~
Đặt \(A=1.2.3.4+2.3.4.5+...+97.98.99.100\)
\(5A=1.2.3.4.5+2.3.4.5.5+...+97.98.99.100.5\)
\(5A=1.2.3.4.5+2.3.4.5.\left(6-1\right)+...+97.98.99.100.\left(101-96\right)\)
\(5A=1.2.3.4.5+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100\)
\(5A=97.98.99.100.101\)
\(A=\frac{97.98.99.100.101}{5}=1901009880\)