18:

a: \(S=3\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{98\cdot100}\right)\)

=3*(1/2-1/4+1/4-1/6+...+1/98-1/100)

=3*49/100=147/100

b: Để A là số nguyên thì n-1 thuộc Ư(2)

=>n-1 thuộc {1;-1;2;-2}

=>n thuộc {2;0;3;-1}

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

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{98.100}\\ =\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\\ =\dfrac{1}{2}-\dfrac{1}{100}\\ =\dfrac{49}{100}\)

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+....+\dfrac{2}{98.100}\)\(=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+....+\dfrac{1}{98}-\dfrac{1}{100}\)

                                                   \(=\dfrac{1}{2}-\dfrac{1}{100}=\dfrac{49}{100}\)

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

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

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

Đặt:

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

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

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

\(3A=49.50.51\)

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

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

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

Đặt 4ra ngoài ta có 8(1+3+6+1225)

 Rồi Tính số số hạng là xong

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

(0,5+0,5)÷0,5_0,5×0,5=