Tính nhanh:
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3+4+....+15}\)
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K
Khách
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Những câu hỏi liên quan
16 tháng 7 2015
\(=\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{64}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(-\frac{3}{4}-\frac{2}{9}-\frac{1}{36}\right)+\frac{1}{64}\)
= 1 + -1 + 1/64
= 0 +1/64
= 1/64
17 tháng 8 2018
C = 1/3 + -3/4 + 3/5 + 1/57 + -1/36 + 1/15 + -2/9
C = ( 1/3 + 1/57 ) + ( -3/4 + -1/36 ) + ( 3/5 + 1/15 ) + -2/9
C = ( 19/57 + 1/57 ) + ( -27/36 + -1/36 ) + ( 9/15 + 1/15 ) + -2/9
C = 20/57 + -28/36 + 10/15 + -2/9
C = 20/57 + -7/9 + 2/3 + -2/9
C = ( 20/57 + 2/3 ) + ( -7/9 + -2/9 )
C = 58/57 + -1
C = 1/57
D = 1/2 + -1/5 + -5/7 + 1/6 + -3/35 + 1/3 + 1/41
D = ( 1/2 + 1/3 + 1/6 ) + ( -1/5 + -5/7 +-3/35 ) + 1/41
D = ( 3/6 + 2/6 + 1/6 ) + ( -7/35 + -25/35 + -3/35 ) + 1/41
D = 1 + -1 + 1/41
D = 1/41
E = -1/2 + 3/5 + -1/9 + 1/127 + -7/18 + 4/35 + 2/7
E = ( -1/2 + -1/9 + -7/18 ) + ( 3/5 + 4/35 ) + 1/127 + 2/7
E = ( -9/18 + -2/18 + -7/18 ) + ( 21/35 + 4/35 ) + 1/127 + 2/7
E = -1 + 5/7 + 1/257 + 2/7
E = -1 + ( 5/7 + 2/7 ) + 1/127
E = -1 + 1 + 1/127
E = 1/127
D
12 tháng 5 2015
Đặt A = \(\frac{\frac{1}{2}}{1+2}+\frac{\frac{1}{2}}{1+2+3}+...+\frac{\frac{1}{2}}{1+2+3+....+100}\)
= \(\frac{1}{2}\left(\frac{1}{2.3:2}+\frac{1}{3.4:2}+\frac{1}{4.5:2}+...+\frac{1}{100.101:2}\right)\)
= \(\frac{1}{2}\left(\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{100.101}\right)\)
= \(\frac{1}{2}.2\left(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\right)\)
= 1\(\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{100}-\frac{1}{101}\right)\)
= \(\frac{1}{2}-\frac{1}{101}=\frac{101}{202}-\frac{2}{202}=\frac{99}{202}\)
HN
19 tháng 8 2016
\(A=\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}=\left(\frac{1}{3}-\frac{2}{9}\right)-\left(\frac{3}{4}+\frac{1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{72}\\ =\frac{1}{9}-\frac{7}{9}+\frac{2}{3}+\frac{1}{72}=-\frac{2}{3}+\frac{2}{3}+\frac{1}{72}=\frac{1}{72}\)
2 tháng 10 2017
\(A=\frac{1}{3}-\frac{3}{4}-\frac{-3}{5}+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
\(\Rightarrow A=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{72}+\frac{-2}{9}+\frac{-1}{36}+\frac{1}{15}\)
\(\Rightarrow A=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(\frac{-3}{4}+\frac{-2}{9}+\frac{-1}{36}\right)+\frac{1}{72}\)
\(\Rightarrow A=1+\left(-1\right)+\frac{1}{72}\)
\(\Rightarrow A=0+\frac{1}{72}\)
\(\Rightarrow A=\frac{1}{72}\)
16 tháng 8 2018
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(\frac{-3}{4}+\frac{-2}{9}+\frac{-1}{36}\right)+\frac{1}{57}\)
\(=\frac{5+9+1}{15}+\frac{\left(-27\right)+\left(-8\right)+\left(-1\right)}{36}+\frac{1}{57}\)
\(=\frac{15}{15}+\frac{-36}{36}+\frac{1}{57}=1-1+\frac{1}{57}=\frac{1}{57}\)
1/1+2 + 1/1+2+3 +1/1+2+3+4 +...+1/1+2+3+...+50
Ta có 2/2(1+2)+2/2(1+2+3)+...+2/2(1+2+...+50)
=2/6+2/12+2/20+...+2/2550
=2/2.3+2/3.4+...+2/50.51
=2(1/2.3+1/3.4+...+1/50.51)
=2(1/1-1/2+1/2-...+1/50-1/51)
=2.(1-1/51)
=2.50/51=100/51