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1: 8=2^3
2: 25=5^2
3: 4=2^2
4: 49=7^2
5: 81=9^2
6: 36=6^2
7: 100=10^2
8: 121=11^2
9: 144=12^2
10: 169=13^2
11: 27=3^3
12: 125=5^3
13: 1000=10^3
14: 32=2^5
15: 243=3^5
16: 343=7^3
17: 216=6^3
18: 64=4^3
19: 225=15^2
20: 128=2^7
\(P=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+...+\frac{1}{121}+\frac{1}{144}\)
\(\Rightarrow P=\frac{1}{4}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{11^2}+\frac{1}{12^2}\)
Ta có : \(P< \frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}+\frac{1}{11.12}\)
\(\Rightarrow P< \frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(\Rightarrow P< \frac{1}{4}+\frac{1}{2}-\frac{1}{12}\)
\(\Rightarrow P< \frac{2}{3}\left(đpcm\right)\)
\(P=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+...+\frac{1}{121}+\frac{1}{144}\)
\(P=\frac{1}{4}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{11^2}+\frac{1}{12^2}\)
Có : \(P< \frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}+\frac{1}{11.12}\)
\(\Rightarrow P< \frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(\Rightarrow P< \frac{1}{4}=\frac{1}{2}-\frac{1}{12}\)
\(\Rightarrow P< \frac{2}{3}\)( đpcm )
Sửa đề : \(S=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{144}\right)\)
\(\Rightarrow S=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{143}{144}\)
\(\Rightarrow S=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{11.13}{12.12}\)
\(\Rightarrow S=\frac{1.2.3.....11}{2.3.4.....12}.\frac{3.4.5.....13}{2.3.4.....12}\)
\(\Rightarrow S=\frac{1}{12}.\frac{13}{2}\)
\(\Rightarrow S=\frac{13}{24}\)
a, A là cộng theo số lẻ ( 1 + 3 = 4 ,4 + 5 = 9.....) bắt đầu từ 3
b , B là mỗi lần cộng thêm 6
c , A là cộng theo số lẻ ( 1 + 3 = 4 ,4 + 5 = 9.....)
d, B là cộng theo số chẵn bắt đầu từ 4
hok tốt
\(a,-\dfrac{4}{5}=-0,8\) \(;\dfrac{2}{10}=0,2\) \(\Rightarrow\) Ko bằng nhau
\(b,\dfrac{3}{2}=1,5;\dfrac{9}{6}=\dfrac{3}{2}=1,5\Rightarrow\) Bằng nhau
\(c,\dfrac{1}{-2}=-0,5;-\dfrac{40}{80}=-\dfrac{1}{2}=-0,5\Rightarrow\) Bằng nhau
\(d,-\dfrac{12}{5}=-2,4;-\dfrac{144}{25}=-5,76\Rightarrow\) Ko bằng nhau
\(e,\dfrac{2525}{4343}=\dfrac{25}{43};\dfrac{25}{43}=\dfrac{25}{43}\)\(\Rightarrow\) Bằng nhau
\(f,-\dfrac{26}{17}\approx-1,53;\dfrac{262626}{171717}=\dfrac{26}{17}\approx1,53\) \(\Rightarrow\) Ko bằng nhau
a) (-37)+14+26+37 = ( -37 + 37) + ( 14 + 26) = 40
b) (-24)+6+10+24 = ( - 24 + 24) + ( 6 + 10) = 16
c) 15+23+9-25)+(-33) = (15 - 25) + ( 23 - 33) + 9
= - 10 - 10 + 9
= - 11
d) 60+33+(-50)+(-33) = ( 60 -50) + ( 33 - 33)
= 10
e) (-16)+(-209)+(-14)+209 = ( - 16 - 14) + ( - 209 + 209)
= - 30
g) (-12)+(-13)+36+(-11)= ( - 11 -12 - 13 ) + 36
= - 36 + 36 = 0
h) -16+24+16-34 = ( - 16 + 16)+(24 - 34) = - 10
r) 25+37-48-25-37 = (25 - 25)+(37 - 37) - 48 = - 48
u) 2575+37-2576-29 = ( 2575 - 2576) + ( 37 - 29)
= - 1 + 8 = 7
i) 34+35+36+37-14-15-16-17 = ( 34 - 14 )+(35 - 15)+(36-16)+ (37 - 17)
= 80
2 . Bỏ ngoặc rồi tính
a)-7264+(1543+7264) = - 7264 + 1543 + 7264
= 1543
b) (144-97)-144 = 144 - 97 - 144 = - 97
c) (-145)-(18-145) = - 145 - 18 + 145 = - 18
d) 11+(-11+27) = 11 - 11 + 27 = 27
e) (27+514)-(486-73) = 27 + 514 - 486 + 73
= 128
g) (36+79)+(145-79-66) = 36 + 79 + 145 - 79 - 66
= 115
h) 10-[12-(-9-1) = 10 - ( 12 + 9 + 1)
= 10 - 22
= - 12
r) (-28-29+43)-(43+38) = - 28 - 29 + 43 - 43 - 38
= - 95
u ) 271 - [(-43)+271-(-17)] = 271 + 43 - 271 - 17 = 26
i ) -144-[29-(+144)-(+144) = - 144 - 29 - 144 + 144 = -173