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tạm thời những bài này bn hãy tính = máy tính , nếu tính bằng giấy sẽ rất mất thì h
b ) \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
= 1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
c ) Đặt A = \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}\)
=> A < \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
=> A < 1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100= 1 - 1/100 = 99/100 < 1
Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}\)< 1
b, \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\)\(\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
c,Ta thấy
\(\frac{1}{2^2}< \frac{1}{1.2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}\)
\(\frac{1}{4^2}< \frac{1}{3.4}\)
\(.....\)
\(\frac{1}{100^2}< \frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)\(< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}< 1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\left(đpcm\right)\)
a: \(\dfrac{A}{B}=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-9\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\)
b: \(\dfrac{C}{D}=\dfrac{3^7\cdot727+3^{12}}{3^{11}+2^3\cdot3^{11}+723\cdot3^6}\)
\(=\dfrac{3^7\left(727+3^5\right)}{3^6\left(3^5+2^3\cdot3^5+723\right)}=\dfrac{1}{3}\cdot3=1\)
bài 1
a) ( 864 . 48 - 432 . 96 ) : 864 . 432 b) ( 7256 . 4375 - 725 ) : ( 3650 + 4375 . 7255 )
=( 41 472-41 472) :864 . 432 = ( 31745000 - 725 ) : ( 3650 + 31740625 )
= ( 0: 864 ) . 432 = 31744275 : 31744275
=0.432=0 =1
bài 2 mik lm sau giúp bn nhé
bài 1
a) ( 864 . 48 - 432 . 96 ) : 864 . 432 b) ( 7256 . 4375 - 725 ) : ( 3650 + 4375 . 7255 )
=( 41 472-41 472) :864 . 432 = ( 31745000 - 725 ) : ( 3650 + 31740625 )
= ( 0: 864 ) . 432 = 31744275 : 31744275
=0.432=0 =1
bài 2 tự làm
1
a) \(\left(20.2^2+12.2^2-48.2^2\right):8^2\)
\(=\left[\left(20+12-48\right).2^2\right]:8^2\)
\(=\left(16.2^2\right):8^2\)
\(=\left(4^2.2^2\right):8^2\)
\(=\left(4.2\right)^2:8^2\)
\(=8^2:8^2\)
= 1