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a/ ta có : 5.(27-17)2 - 611 : 69 = 5.102 - 611 :69
= 5.100 - 611-9 = 500 - 36 = 464
b/ ta có : (-15)+(-17) = -15 - 17 = -32
c/ ta có : 21.42 + 21.59 +21.52 = 21.(42 +59 +52 )
= 21. (16 + 59 + 25) = 21.100=2100
d/ ta có : 75 - (3.52 - 4.23 ) +20150 = 75 - (3.25 - 4.8) +1
= 75 - 43 +1 = 33
a, [(52 - 43)2 - (137 - 131)2] : 5
=[81 - 36] : 5
=45 : 5
= 9
b, 549 :(34 - 22 . 5) - 9
= 549 : (81 - 4 . 5) -9
= 549 : (81 - 20) -9
= 549 : 61 -9
= 9 - 9
= 0
mình ko biết viết ngoặc nên bạn thêm vào chỗ cần thiết nhé!
a. 92- (137- 131)2 chia
92- 62 chia 5
81- 36 chia 5
45 chia 5
9
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
\(\frac{1}{2^2}< \frac{1}{1.2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}\)
\(\frac{1}{4^2}< \frac{1}{3.4}\)
\(.....\)
\(\frac{1}{100^2}< \frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)\(< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}< 1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\left(đpcm\right)\)
#)Giải :
a)\(9^2\div\left(27^3.81^2\right)=9^2\div\left[\left(3^3\right)^3.\left(9^2\right)^2\right]=9^2\div\left(3^9.9^4\right)\)
Tự lm típ
a,\(9^2:\left(27^3.81^2\right)=3^4:\left(3^9.3^8\right)=3^4:\left(3^{9+8}\right)=3^4:3^{17}=3^{-13}\)
\(3^3\cdot5^3-20\cdot\left\{300-\left[546-2^3\cdot\left(7^8-7^6+7^0\right)\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300-\left[546-2^3\cdot5647153\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300-\left[546-45177224\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300--45176678\right\}\)
\(=3^3\cdot5^3-20\cdot45176978\)
\(=3375-903539560\)
\(=-903536185\)
\(626500:\left\{50^2:\left[178-4\cdot\left(35-21:3\right)\right]\right\}\)
\(=626500:\left\{50^2:\left[178-4\cdot\left(35-7\right)\right]\right\}\)
\(=626500:\left\{50^2:\left[178-4\cdot28\right]\right\}\)
\(=626500:\left\{50^2:\left[178-112\right]\right\}\)
\(=626500:\left\{50^2:66\right\}\)
\(=626500:\frac{1250}{33}\)
\(=\frac{82698}{5}\)
CHUC BAN HOC TOT >.<
a) 36 : 32 + 23 . 34
= ( 36-2) + 8 . 81
= 34 + 648
= 81 + 648
= 729
b) 21 . { 108 : 9 -[ 235 - ( 273 - 43)]}
= 21 . { 108 : 9 -[ 235 - 230 ] }
= 21 . { 108 :9 - 5 }
= 21 . {12 - 5 }
= 21 . 7
= 147
^^
\(a,3^6:3^2+2^3.3^4=3^4+8.3^4=9.3^4=729\)