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= 1/1x2 + 1/2x3 + 1/3x4 ...... +1/9x10
= 1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10
=1-1/10=9/10
đặt A=1/1 x 1/2 + 1/2 x 1/3 + 1/3 + 1/4 + .......... + 1/9 x 1/10
\(A=\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+...+\frac{1}{9}\cdot\frac{1}{10}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
đặt B=2/1 x 2 + 2/2 x 3 + 2/3 x4 + .............. + 2/98 x 99 + 2/99 x 100
\(B=2\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=2\left(1-\frac{1}{100}\right)\)
\(=2\times\frac{99}{100}\)
\(=\frac{99}{50}\)
A = ( 1- 1/95 ) x ( 1 - 1/96 ) x ( 1-1/97 ) x ( 1-1/98 ) x ( 1 - 1/99 ) tính thuận tiện nhé giúp với
A = (1 - 1/95) . ( 1 - 1/96) . (1 - 1/97) . (1 - 1/98) . ( 1 - 1/99)
A = 94/95 . 95/96 . 96/97 . 97/98 . 98/99
A = \(\dfrac{94.95.96.97.98}{95.96.97.98.99}\)
A = 94/99
Vậy A = 94/99
- HokTot -
\(A=\left(1-\dfrac{1}{95}\right)\times\left(1-\dfrac{1}{96}\right)\times\left(1-\dfrac{1}{97}\right)\times\left(1-\dfrac{1}{98}\right)\times\left(1-\dfrac{1}{99}\right)\)
\(A=\dfrac{94}{95}\times\dfrac{95}{96}\times\dfrac{96}{97}\times\dfrac{97}{98}\times\dfrac{98}{99}\)
\(A=\dfrac{94\times95\times96\times97\times98}{95\times96\times97\times98\times99}\)
\(A=\dfrac{94}{99}\) (gạch bỏ những số giống nhau)
Bài 3:
= 1- 1/2 + 1/2 -1/3 +...+ 1/98 -1/99
= 1- 1/99
= 98/99
Bài 4:
= 1/2*3 + 1/3*4 + 1/4*5 +...+ 1/10*11
= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +...+ 1/10 - 1/11
= 1/2 - 1/11= 9/22
(1+1/2)x(1+1/3)x(1+1/4)x....x(1+1/98)x(1+1/99)
=3/2x4/3x5/4x..........x99/98x100/99
=(3x4x5x........x99x100)/2x3x4x........x98x99
Giản ước ta được:
=100/2
=50
B=3/2x4/3x...........x2018/2017
=3x4x5x...........x2018/2x3x2x2x............x2017
=2x2018
=4036
A,C tương tự
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)
\(=\frac{100}{2}=50\)