Tính nhanh:
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.......+\frac{1}{1+2+3+4+....+15}\)
THANKS
Tính nhanh
\(\frac{1}{3}-\frac{3}{4}-\left(-\frac{3}{5}\right)+\frac{1}{64}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
Các bạn vui lòng giải đầy đủ giúp mình. Thanks trước!
\(=\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{64}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(-\frac{3}{4}-\frac{2}{9}-\frac{1}{36}\right)+\frac{1}{64}\)
= 1 + -1 + 1/64
= 0 +1/64
= 1/64
BÀi 1: Thực hiện phép tính ( tính nhanh nếu có thể)
a.\(\left(-\frac{1}{2}\right)-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{71}-\left(-\frac{2}{7}\right)+\frac{4}{35}-\frac{7}{18}\)
b.\(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5-\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
c.\(\frac{3}{5}:\left(\frac{-1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{1}{3}-1\frac{1}{15}\right)\)
Tính nhanh :
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(D=\frac{1}{2}+\frac{-1}{5}+\frac{-5}{7}+\frac{1}{6}+\frac{-3}{35}+\frac{1}{3}+\frac{1}{41}\)
\(E=\frac{-1}{2}+\frac{3}{5}+\frac{-1}{9}+\frac{1}{127}+\frac{-7}{18}+\frac{4}{35}+\frac{2}{7}\)
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
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}.\)
\(C=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{1}{36}+\frac{2}{9}\right)+\frac{1}{57}\)
\(C=1-1+\frac{1}{57}\)
\(C=\frac{1}{57}\)
D=1/2+-1/5+-5/7+1/6+-3/35+1/3+1/41
D=(1/2+1/6+1/3)-(1/5+3/35+5/7)+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=(3/5+4/35+2/7)-(1/2+1/9+7/18)+1/127
E=1-1+1/127
E=1/127
Bài 1 : tính nhanh
a) \(A=\frac{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}:\frac{3+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}}{2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}}\)
Các bn giúp mik nhá
Tính nhanh \(1-\frac{1}{2}+2-\frac{2}{3}+3-\frac{3}{4}+4-\frac{1}{4}-3-\frac{1}{3}-2-\frac{1}{2}-1=?\)
Tính nhanh:\(\frac{\frac{1}{2}}{1+2}+\frac{\frac{1}{2}}{1+2+3}+\frac{\frac{1}{2}}{1+2+3+4}+...+\frac{\frac{1}{2}}{1+2+3+4+...+100}\)
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\(\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{100}-\frac{1}{101}\right)\)
= \(\frac{1}{2}-\frac{1}{101}=\frac{101}{202}-\frac{2}{202}=\frac{99}{202}\)
Bài 2 : Tính nhanh
a= \(\frac{1}{3}-\frac{3}{4}-\left(-\frac{3}{5}\right)+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
\(A=\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}=\left(\frac{1}{3}-\frac{2}{9}\right)-\left(\frac{3}{4}+\frac{1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{72}\\ =\frac{1}{9}-\frac{7}{9}+\frac{2}{3}+\frac{1}{72}=-\frac{2}{3}+\frac{2}{3}+\frac{1}{72}=\frac{1}{72}\)
Tính nhanh:
\(A=\frac{1}{3}-\frac{3}{4}-\frac{-3}{5}+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
\(A=\frac{1}{3}-\frac{3}{4}-\frac{-3}{5}+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
\(\Rightarrow A=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{72}+\frac{-2}{9}+\frac{-1}{36}+\frac{1}{15}\)
\(\Rightarrow A=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(\frac{-3}{4}+\frac{-2}{9}+\frac{-1}{36}\right)+\frac{1}{72}\)
\(\Rightarrow A=1+\left(-1\right)+\frac{1}{72}\)
\(\Rightarrow A=0+\frac{1}{72}\)
\(\Rightarrow A=\frac{1}{72}\)
Tính nhanh :
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)+\left(\frac{-3}{4}+\frac{-2}{9}+\frac{-1}{36}\right)+\frac{1}{57}\)
\(=\frac{5+9+1}{15}+\frac{\left(-27\right)+\left(-8\right)+\left(-1\right)}{36}+\frac{1}{57}\)
\(=\frac{15}{15}+\frac{-36}{36}+\frac{1}{57}=1-1+\frac{1}{57}=\frac{1}{57}\)