Tính hợp lí
1/200- 1/200.199-1/199.198-.....-1/3.2-1/2.1
Tính hợp lí
1/200- 1/200.199- 1/199.198- .....-1/3.2- 1/2.1
\(\frac{1}{200}-\frac{1}{200.199}-\frac{1}{199.198}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{200}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{198.199}+\frac{1}{199.200}\right)\)
\(=\frac{1}{200}-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{198}-\frac{1}{199}+\frac{1}{199}-\frac{1}{200}\right)\)
\(=\frac{1}{200}-\left(1+\frac{1}{200}\right)\)
\(=\left(\frac{1}{200}-\frac{1}{200}\right)-1\)
\(=0-1\)
\(=-1\)
tính 1/200-(1/200.199-1/199.198-...-1/2.1)
\(\frac{1}{200}-\left(\frac{1}{200.199}-\frac{1}{199.198}-...-\frac{1}{3.2}-\frac{1}{2.1}\right)\)]
Giúp mình với
\(\frac{1}{200}-\left(\frac{1}{200.199}-\frac{1}{199.198}-...-\frac{1}{3.2}-\frac{1}{2.1}\right)\)
giúp mình với mai mình đi hc rồi
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hoặc bạn sang trang 3 của hỏi đáp toán hoc24 sẽ thấy nhé
tinh gia tri cua bieu thuc sau :
A=1/199-1/199.198-1/198.197-1/197.196-.............-1/3.2-1/2.1
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 ~
Tính giá trị biểu thức sau:
a, A=1/199 - 1/199.198 - 1/198.197 - 1/197.196 -....- 1/3.2 - 1/2.1
b, B=1- 2/3.5- 2/5.7- 2/7.9 -...- 2/61.63 - 2/63.65
tính hợp lí 1/99 - 1/99.98 - 1/98.97 - 1/ 97.96 - ... -1/3.2 - 1/2.1
\(\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}-\frac{1}{97.96}+......+\frac{1}{2.1}\)
= \(\frac{1}{99}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{98.99}\right)\)
= \(\frac{1}{99}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{98}-\frac{1}{99}\right)\)
= \(\frac{1}{99}-\left(1-\frac{1}{99}\right)\)
= \(\frac{1}{99}-\frac{98}{99}\)
= \(\frac{-97}{99}\)
tính hợp lí nếu có thể
1/2014-1/2014.2013-1/2013.2012-...-1/3.2-1/2.1
\(=\frac{1}{2014}-\frac{2014-2013}{2014.2013}-\frac{2013-2012}{2013.2012}-...-\frac{3-2}{3.2}-\frac{2-1}{2.1}\)
\(=\frac{1}{2014}-\left(\frac{2014}{2014.2013}-\frac{2013}{2014.2013}\right)-...-\left(\frac{3}{3.2}-\frac{2}{3.2}\right)-\left(\frac{2}{2.1}-\frac{1}{2.1}\right)\)
\(=\frac{1}{2014}+\left(\frac{1}{2014}-\frac{1}{2013}\right)+...+\left(\frac{1}{3}-\frac{1}{2}\right)+\left(\frac{1}{2}-1\right)\)
\(=\frac{1}{1007}-1\)
\(=\frac{-1006}{1007}\)
TÍNH HỢP LÍ( NẾU CÓ THỂ)
\(\frac{1}{2014}-\frac{1}{2014.2013}-\frac{1}{2013.2012}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(\frac{1}{2014}-\frac{1}{2014.2013}-\frac{1}{2013.2012}-...-\frac{1}{3.2}-\frac{1}{2.1}.\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2012.2013}+\frac{1}{2013.2014}\right)+\frac{1}{2014}\)
\(=\frac{1}{2014}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)
\(=\frac{1}{2014}-1+\frac{1}{2014}=\frac{1}{1007}-1=\frac{-1006}{1007}\)
....