(1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)
(1-1/4)*(1-1/9)*(1-16)*(1-1/25)*(1-1/36)
tinh nhanh
Những câu hỏi liên quan
tinh nhanh
K = [ 1-1/4 ] x [ 1-1/9 ] x [ 1-1/16 ] x [ 1-1/25 ] x [ 1-1/36 ]
Câu 15 A= 1/3-3/4+3/5+1/2007-1/36+1/25-2/9
Câu 16 A=1/3- 3/4- (-3/5)+ 1/64- 2/9- 1/36+ 1/15
Câu 17 A=1/2- 2/3+ 3/4- 4/5+ 5/6- 6/7- 5/6+ 4/5- 3/4+ 2/3- 1/2
15: A= 1/3-3/4+3/5+1/2007-1/36+1/15-2/9
Sửa đề:
A=-3/4-2/9-1/36+1/3+3/5+1/15+1/2007
=-27/36-8/36-1/36+5/15+9/15+1/15+1/2007
=-1+1+1/2007=1/2007
16:
\(A=\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}\)
=1/64
17:
=1/2-1/2+2/3-2/3+3/4-3/4+4/5-4/5+5/6-5/6-6/7
=-6/7
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Tính hợp lí nếu có thể:
a)3/7+4/9+4/7+5/9
b)1/5+4/10+9/15+16/20+25/25+36/30+49/35+64/40+81/45
c)1/8+1/12+3/8+5/12
d)(1-1/2)x(1-1/3)x(1-1/4)x...x(1-100)
e)9/5:17/15+8/5:17/15
f)2/1x2+2/2x3+2/3x4+...+2/19x20
Ai nhanh nhất mình tick cho
a) 3/7 + 4/9 + 4/7 + 5/9
= ( 3/7 + 4/7 ) + ( 4/9 + 5/9 )
= 7/7 + 9/9
= 1 + 1
= 2
b)1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45
= 1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5
= ( 1/5 + 9/5 ) + ( 2/5 + 8/5 ) + (7/5 + 3/5 ) + ( 4/5 + 6/5 ) + 5/5
= 2 + 2 + 2 + 2 + 1
= 2 x 4 + 1
= 8 +1
= 9
c) 1/8 + 1/12 + 3/8 + 5/12
= ( 1/8 + 3/8 ) + ( 1/12 + 5/12)
= 4/8 + 6/12
= 1/2 + 1/2
= 2/4 = 1/2
mỏi tay rồi
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Tính nhanh:
a,1/4+2/5+6/8+9/15+8/1
b,1/2+2/4+3/6+4/8+5/10+6/12+7/14+8/16+9/18+10/20
c,1/10+4/20+9/30+16/40+25/50+36/60+49/70+64/80+81/90
Tính nhanh:
a,1/4+2/5+6/8+9/15+8/1
b,1/2+2/4+3/6+4/8+5/10+6/12+7/14+8/16+9/18+10/20
c,1/10+4/20+9/30+16/40+25/50+36/60+49/70+64/80+81/90
Tính nhanh
( 1-1/4)*(1-1/9)*(1-1/16)*(1-1/25)*(1-1/36)
T
cho A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81 . Chứng tỏ A > 2/5
A=1/22+1/32+...+1/92
Ta có:1/22>1/2.3,1/32>1/3.4,...,1/92>1/9.10
⇒A>1/2.3+1/3.4+...+1/9.10
A>1/2-1/3+1/3-1/4+...+1/9-1/10
A>1/2-1/10
A>2/5(đpcm)
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Ta có: A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81
Vì 1/22>1/2.3,1/32>1/3.4,...,1/92>1/9.10
=>A>1/2.3+1/3.4+...+1/9.10
=>A>1/2-1/3+1/3-1/4+...+1/9-1/10
=>A>1/2-1/10
=>A>2/5
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Giải:
\(A=\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{25}+\dfrac{1}{36}+\dfrac{1}{49}+\dfrac{1}{64}+\dfrac{1}{81}\)
\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2} +\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}+\dfrac{1}{9^2}\)
Ta có:
\(\dfrac{1}{2^2}=\dfrac{1}{2.2}>\dfrac{1}{2.3}\)
\(\dfrac{1}{3^2}=\dfrac{1}{3.3}>\dfrac{1}{3.4}\)
\(\dfrac{1}{4^2}=\dfrac{1}{4.4}>\dfrac{1}{4.5}\)
\(\dfrac{1}{5^2}=\dfrac{1}{5.5}>\dfrac{1}{5.6}\)
\(\dfrac{1}{6^2}=\dfrac{1}{6.6}>\dfrac{1}{6.7}\)
\(\dfrac{1}{7^2}=\dfrac{1}{7.7}>\dfrac{1}{7.8}\)
\(\dfrac{1}{8^2}=\dfrac{1}{8.8}>\dfrac{1}{8.9}\)
\(\dfrac{1}{9^2}=\dfrac{1}{9.9}>\dfrac{1}{9.10}\)
\(\Rightarrow A>\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{10}\)
\(\Rightarrow A>\dfrac{2}{5}\left(đpcm\right)\)
Chúc bạn học tốt!
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tinh nhanh :
Xem chi tiết
a) 5/6 x 11/4 - 5/4 x 23/6
b) 9/16 x 13/4 - 9/4 x 5/16 + 9/16 x 17/
hay tinh tong:
1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/n (n + 1)
chung minh:
1/22 + 1/32 + 1/42 + ..... + 1/n2 < 1
giai dum nhe
Bài 1: Tìm x:a) x - 2 + 7 = 1 . 3 . -9 b) 4 . x - 1 = (-5) 5 12 2 4 16 9 2 9c) -2 . x + 5 = 7 d) 2 . x : 7 . 1 = 29 3 8 12 5 3 8 15Bài 2: Tính:a) 2 + 1 . 4 b) 0,8 : [ 4 . 1,25] - [ 0,64 - 1 ] 5 7 5 25--------------------- 8 - 1 : 3 2 5 c) 8 : [ 7 - 12 ] d) ( 1,08 - 2 ) : 4 + ( 59 - 13 ). 36 9 2 7 25 7 9 4 17----------------------- [ 5 - 1 ] : 4