(1/2+2/3+3/4+4/5+...+122/123+123/124).(125-5.25)

=(1/2+2/3+3/4+4/5+...+122/123+123/124).(125-125)

=(1/2+2/3+3/4+4/5+...+122/123+123/124).0=0

15

694

357

67

35

369

15
694
67
35
369

1+2+3+4+5=15
123+571=694
109+248=357
190-123=67
187-152=35
123+246=369

1 - 1/2 + 1/3 - 1/4 + .. + 1/121 - 1/122 + 1/123

=  ( 1 + 1/3 + ... + 1/121 + 1/123 ) - ( 1/2 + 1/4 + .. + 1/122 ) 

Đến bước này ta sẽ cùng cộng 2 vế với : 1/2 + 1/4 + .. + 1/122 

=   ( 1 + 1/2 + 1/3 + 1/4 + ...+ 1/121 + 1/122 + 1/123 ) - 2. ( 1/2 + 1/4 + .. + 1/122 )

=    (  1 + 1/2 + 1/3 + ...+ 1/122 +1 /123 )  -  (  1 + 1/2 + ...+ 1/61 ) 

=                   1/62 + 1/63 + ..+1/122 + 1/123 

Chúc học giỏi !!

Lời giải:

a)

\(A=75^2+50.75+25^2=75^2+2.25.75+25^2\)

\(=(75+25)^2=100^2=10000\)

b) \(123^2+23^2-46.123=123^2-2.23.123+23^2\)

\(=(123-23)^2=100^2=10000\)

c) \((3^4-1)(3^4+1)-9^4\)

\(=[(3^4)^2-1^2]-9^4=(9^4-1)-9^4=-1\)

a) \(=\frac{3}{17}-\frac{2}{345}+\frac{5}{12}+\frac{2}{345}-\frac{3}{17}+\frac{1}{12}\)

\(=\left(\frac{3}{17}-\frac{3}{17}\right)+\left(\frac{2}{345}-\frac{2}{345}\right)+\left(\frac{5}{12}+\frac{1}{12}\right)\)

\(=\frac{6}{12}=\frac{1}{2}\)

b) \(=-\frac{49}{25}-\frac{5}{36}+\frac{4}{123}+\frac{49}{25}-\frac{4}{123}-\frac{1}{36}\)

\(=\left(-\frac{49}{25}+\frac{49}{25}\right)+\left(\frac{4}{123}-\frac{4}{123}\right)-\left(\frac{5}{36}+\frac{1}{36}\right)\)

\(=-\frac{6}{36}=-\frac{1}{6}\)

Cảm ơn

Tính nhanh:

 1+2+3+4+5+6+7+8+9+10

=(1+9)+(2+8)+(3+7)+(4+6)+10+5

=  10  +  10  +  10   + 10  + 10+5

=             50   +   5

=    55

123*45+123*50+123*5

=  123*(45+50+5)

=   123 * 100

=   12300

K mk nha bn

1+2+3+4+5+6+7+8+9+10

= ( 1+10 ) + ( 2+9) + (3+8) + (4+7) + (5+6)

=     11    +      11   +   11    +   11  +    11

=11 x 5 

=55

123 x 45 + 123 x 50 + 123 x 5 

= 123 x ( 45 + 50 +5 )

= 123 x 100

=12300

hok tốt .

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 10 : 2 x 11 = 55

123 x 45 + 123 x 50 + 123 x 5 = 123x ( 45 + 50 + 5) = 123 x 100 = 12300

\(\frac{4.\left(\frac{1}{5}-\frac{1}{71}+\frac{1}{123}\right)}{3.\left(\frac{1}{5}-\frac{1}{71}+\frac{1}{123}\right)}-\frac{\frac{1}{19}+\frac{1}{1315}-\frac{1}{287}}{3.\left(\frac{1}{19}+\frac{1}{1315}-\frac{1}{287}\right)}=\frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1\)