mình k viết lại đề nhé =)

câu A

A :5 =1/2.4+1/4.6+1/6.8+..+1/98.100

A:5 =1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100

A:5 =1/2-1/100 =49/100

A=49/100 x5 =49/20

câu B tươg tự nha =)

Ta có:

A =5/2(1/2-1/4 + 1/4-1/6+ 1/6..........1/98-1/100)

A =5/2 (1/2 -1/100)

A =5/2 x 49/100

A = 49/20

A=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2)

A=1.2.4+2.3.4+...+50.51.4

A=4(1.2+2.3+...+50.51)

M= 1.2+2.3+...+50.51

3M=1.2.3+2.3.(4-1)+...+50.51.(52-49)

=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51

= 50.51.52

=132600

=> M=44200

=> A=4M=176800

\(B=2.4+4.6+6.8+...+98.100\)

\(B=2.\left(1.2\right)+2.\left(2.3\right)+2.\left(3.4\right)+...+2.\left(49.50\right)\)

\(B=2\left(1.2+2.3+3.4+....+49.50\right)\)

Đặt:

\(A=1.2+2.3+3.4+...+49.50\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)

\(3A=49.50.51\)

\(A=\dfrac{49.50.51}{3}=41650\)

\(B=2A=41650.2=83300\)

Câu 1:

A = 2.4 + 4.6 + 6.8 +...+ 98.100 + 100.102

6A = 2.4.6 + 4.6.6 +..+98.100.6 + 100.102.6

6A = 2.4.6 + 4.6.(8-2) +...+100.102.(104 - 98)

6A = 2.4.6 + 4.6.8 - 2.4.6 + ...+ 100.102.104 - 98.100.102

6A = 100.102.104

A = 100.102.104 : 6

A = 10200.104 : 6

A = 1060800 : 6

A = 176800

Câu 2:

B = 1.3 + 3.5 + 5.7 + ...+ 97.99 + 99.101

6B = 1.3.6 + 3.5.6 + ...+ 99.101.6

6B = 1.3.(5+1) . 3.5.(7-1) + ..+99.101.(103-97)

6B = 1.3.5 + 1.3.1 +3.5.7- 1.3.5 +...+99.101.103 - 97.99.101

6B = 1.3.1 + 99.101.103

6B = 3 + 9999.103

6B = 3 + 1029897

6B = 1029900

B = 1029900 : 6

B = 171650

6A = 2 . 4 . 6 + 4.6.6 + 6.8.6 + ... + 98 . 100 . 6 = 2.4.6 + 4.6.(8-2) + ... + 98. 100 . (102 - 96)

                                                                           = 2.4.6 +4.6.8 - 2.4.6 + .... + 98.100 . 102 - 96.98.100

                                                                            = 98. 100 . 102

                                                                            = 999600

Suy ra A = 166600

Vậy ______________________

=166600

\(\frac{2.4+4.6+6.8+...+98.100}{1.2+2.3+3.4+...+49.50}=\frac{4.\left(1.2+2.3+3.4+...+49.50\right)}{1.2+2.3+3.4+...+49.50}=\frac{4}{1}=4\)

(0,5+0,5)÷0,5_0,5×0,5=

D = 2.4 + 3.5 + 4.6 + 5.7 + 6.8 + 7.9 + ...+ 97.99 + 98.100

D = (2.4 + 4.6 +...+ 98.100) + (3.5 + 5.7 + 7.9 + ..+ 97.99)

Đặt A = 2.4 + 4.6 +...+ 98.100

B = 3.5 + 5.7 + 7.9 + ..+ 97.99

Khi đó: D = A + B

Xét tổng A : A = 2.4 + 4.6 + ..+ 98.100

6A = 2.4.6 + 4.6.6 + ...+ 98.100.6

6A = 2.4.6 + 4.6.(8 - 2) +...+ 98.100.(102-96)

6A = 2.4.6 + 4.6.8 - 2.4.6 + ...+ 98.100.102 - 96.98.100

6A = 98.100.102

A = 98.100.102 : 6

A = 166600

Xét tổng B = 3.5 + 5.7 + ...+ 97.99

6B = 3.5.6 + 5.7.6 + ..+ 97.99.6

6B = 3.5.(7- 1) + 5.7.(9 - 3) + ...+ 97.99.(101 - 95)

6B = 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 97.99.95

6B = - 1.3.5 + 97.99.101

6B = - 15 + 969903

6B = 969888

B = 969888 : 6

B = 161648

D = A + B

D = 166600 + 161648

D = 328248

\(\frac{6}{2.4}+\frac{6}{4.6}+...+\frac{6}{98.100}\)

= \(\frac{6}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)

= \(3.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

= \(3.\left(\frac{1}{2}-\frac{1}{100}\right)\)

= \(3.\frac{49}{100}\)

= \(\frac{147}{100}\)