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1-2-3+4+5-6-7+8+...+21-22-23+24
= ( 1-2-3 + 4) + ( 5-6-7+8)+...+(21 -22- 23 +24)
= 0+0 +....+0
= 0
1 - 2 - 3 + 4 + 5 - 6 - 7 + 8 + . . . + 21 - 22 - 23 + 24
= ( 1 - 2 - 3 + 4 ) + ( 5 - 6 - 7 + 8 ) + . . . + ( 21 - 22 - 23 + 24 )
= 0 + 0 + . . . + 0
= 0
ta thấy : 1/21>1/33;...1/30>1/33
Vậy 1/21+..+1/30>1/33+...+1/33(10 lần 1/33)
1/3=11/33
mà 1/33+..+1/33(10 lần 1/33) =10/33
Suy ra S>1/33+..+1/33(10 lần 1/33)>1/3
Vậy S>1/3
nhớ k nha bạn
\(A=47.36+64.47+15\)
\(A=47.\left(36+64\right)+15\)
\(A=47.100+15\)
\(A=4700+15\)
\(A=4715\)
\(B=27+35+65+73+75\)
\(B=\left(27+73\right)+\left(35+65\right)+75\)
\(B=100+100+75\)
\(B=275\)
\(C=37+37.15+84.37\)
\(C=37.\left(1+15+84\right)\)
\(C=37.100\)
\(C=3700\)
\(D=\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+\frac{1}{23.24}\)
\(D=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+\frac{1}{23}-\frac{1}{24}\)
\(D=\frac{1}{20}-\frac{1}{24}\)
\(D=\frac{24}{480}-\frac{20}{480}\)
\(D=\frac{4}{480}=\frac{1}{120}\)
\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(E=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=1-\frac{1}{50}\)
\(E=\frac{49}{50}\)
A = 47 x 36 + 64 x 47 + 15
A= 47 x ( 64 + 36 ) + 15 = 47 x 100 + 15 = 4700 + 15 = 4715
vậy A= 4715
B= 27+35 + 65 + 73+ 75
B= (27+ 73) + ( 35 + 65) +75
B= 100 +100 +75 = 275
vậy B= 275
C= 37 +37 x 15 +37 x 84
C= 37 x ( 1+15 +84 )= 37 x 100 = 3700
vậy C= 3700
D = 1/20x21 + 1/21x22 + 1/22x23 + 1/23x24
D= 1/20 - 1/21 + 1/21 - 1/22 + 1/22 - 1/23 + 1/23 - 1/24
D= 1/20 -1/24 = 1/120 vậy D= 1/120
E= 1/1x2 + 1/2x3 + ...... + 1/49x50
E= 1/1 - 1/2 + 1/2 - 1/3 +...... + 1/49 - 1/50
E = 1 - 1/50 = 49/50
vậy E= 49/50
CHÚC HOK TOT
\(S=\frac{1}{21}+\frac{1}{22}+...+\frac{1}{150}\)
\(=\left(\frac{1}{21}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+...+\frac{1}{80}\right)+\left(\frac{1}{81}+...+\frac{1}{150}\right)\)
\(>\left(\frac{1}{40}+...+\frac{1}{40}\right)+\left(\frac{1}{80}+...+\frac{1}{80}\right)+\left(\frac{1}{150}+...+\frac{1}{150}\right)\)
\(=\frac{20}{40}+\frac{40}{80}+\frac{70}{150}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{7}{15}>\frac{5}{4}\)
a, 23 + ( -77 ) + ( -23 ) + 77
= [ 23 + ( -23 ) ] + [ ( -77 ) + 77 ]
= 0 + 0 = 0
b, ( -2020 ) + 2021 + 21 + ( -22 )
= ( - 2020 ) + 2021 + 21 + ( -21 ) + ( -1 )
= [ ( -2020 ) + 2021 + ( -1 ) ] + [ 21 + ( -21 ) ]
= 0 + 0 = 0
1+2^1+2^2+2^3+2^4+...+2^20
=2*(1+2^1+2^2+2^3+2^4+...+2^20)-1-2^1+2^2-2^3-2^4-...-2^20
=2^1+2^2+2^3+2^4+...+2^21-1-21-2^2-2^3-2^4-...-2^21
=2^21-1