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Bài 1: So sánh
a)\(^{56^{56}-56^{56}}\)và \(^{56^{56}-56^{54}}\)
b)\(3^5.7^{15}\) và \(27^5.7^{16}\)
a, ta có:VT=0 \(\Rightarrow56^{56}-56^{56}< 56^{56}-56^{54}\)
b,Ta có:\(27^5.7^{16}=(3^3)^5.7^{16}\)\(\Leftrightarrow3^{15}.7^{16}\)
nhận thấy:\(3^5< 3^{15}\);\(7^{15}< 7^{16}\)
\(\Rightarrow3^5.7^{15}< 27^5.7^{16}\)
Sửa đề: A=-1/20+(-1/30)+(-1/42)+(-1/56)+(-1/72)+(-1/90)
=-(1/20+1/30+...+1/90)
=-(1/4-1/5+1/5-1/6+...+1/9-1/10)
=-1/4+1/10
=-5/20+2/20=-3/20
24.(56-45)+56.(-24-45)
= 24.56-24.45-56.24-56.45
= (24.56-56.24)-(24.45+56.45)
= 0-45.(24+56)
= -45.80
= -3600
24 . (56 - 45) + 56(-24 - 45)
= 24 . 56 - 24 . 45 + 56 . (-24) - 56 . 45
= [24 . 56 + 56 . (-24)] - (24 . 45 + 56 . 45)
= 56 . [24 + (-24)] - 45(24 + 56)
= 56 . 0 - 45 . 80 = 0 - 3600 = -3600
A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8
A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8
A = 1 + ( -1/2 + 1/2 ) + ( -1/3 + 1/3 ) + ( -1/4 + 1/4 ) + ( -1/5 + 1/5 ) + ( -1/6 + 1/6 ) + ( -1/7 + 1/7 ) - 1/8
A = 1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8
A = 1 - 1/8
A = 7/8
* Sửa đề tí nhé
B = 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56
B = 3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8
B = 3 - 3/2 - 5/2 - ( -5/3 ) + 7/3 - 7/4 - 9/4 - ( -9/5 ) + 11/5 - 11/6 - 13/6 - ( -13/7 ) + 15/7 - 15/8
B = 3 - 3/2 - 5/2 + 5/3 + 7/3 - 7/4 - 9/4 + 9/5 + 11/5 - 11/6 - 13/6 + 13/7 + 15/7 - 15/8
B = 3 + ( -3/2 - 5/2 ) + ( 5/3 + 7/3 ) + ( -7/4 - 9/4 ) + ( 9/5 + 11/5 ) + ( -11/6 - 13/6 ) + ( 13/7 + 15/7 ) - 15/8
B = 3 + -4 + 4 + -4 + 4 + -4 + 4 - 15/8
B = 3 + 0 + 0 + 0 - 15/8
B = 3 - 15/8
B = 9/8
Sửa đề thành \(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{132}\)
\(=\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{11.12}\)
\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{11}-\dfrac{1}{12}\)
\(=\dfrac{1}{5}-\dfrac{1}{12}=\dfrac{7}{60}\)
1/20+1/30+1/42+1/56+1/72
=1/4x5+1/5x6+1/6x7+1/7x8+1/8x9
=1/4-1/5+1/5-1/6+...+1/9
=1/4-1/9
= 5 / 36
= 1/4x5 + 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9
=1/4 - 1/5 + 1/5 - 1/6 +... + 1/8 - 1/9
= 1/4 - 1/9 = 5/36
\(1-56=-55\)
1-56=-55