A = (13x+5a)+(21b-3b) = 18a+18b = 18.(a+b) = 18.100 = 1800

B = (1+100).100 : 2 = 5050

Tk mk nha

A=13a+21b+5a-3b

A=(13a+5a)+(21b-3b)

A=18a+18b

A=18.(a+b)

tha a+b+100ta được:

A=18.100

A=1800

B=1+2+3+...+99+100

số số hạng của tổng Blà(100-1):1+1=100

vậy B=(100+1).100:2=5050

C=1.2+2.3+3.4+...+99.100

3C=1.2.3+2.3.3+3.4.3+...+99.100.3

3C=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

3C=(1.2.3+2.3.4+3.4.5+...+99.100.101)-(0.1.2+1.2.3+2.3.4+...+98.99.100)

3C=99.100.101-0.1.2

3C=999900-0

3C=999900

C=999900:3

C=333300

c, 4C= (1.2.3+2.3.4+3.4.5+...+8.9.10) .4

==> 4C= [1.2.3.(4-0) + 2.3.4-(5-1) + 8.9.10.(11-7)

==>4C= 1.2.3.4 - 1.2.3.4+ 2.3.4.5-2.3.4.5 + 7.8.9.10- 7.8.9.10 + 8.9.10.11

==> 4C= 8.9.10.11=7920

==> C= 7920 :4=1980

a, Ta có: 3A= 1.2.3+2.3.3+3.4.3+...+99.100.3

               3A=1.2.(3-0) + 2.3.(4-1)+ 3.4.(5-2)+ ... + 99.100.( 101-98)

               3A=(1.2.3 + 2.3.4+ 3.4.5+ 99.100.101) - (0.1.2 +1.2.3+ 2.3.4 + ... + 98.99.100)

               3A= 99.100.101 - 0.1.2

               3A= 999900 - 0

               3A= 999900

    ==> A= 999900 : 3

   ==> A= 333300

c) Đặt \(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)

Ta có: \(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)

\(\Leftrightarrow3A=3\cdot\left(1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\right)\)

\(\Leftrightarrow3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(\Leftrightarrow3\cdot A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+...+98\cdot99\cdot100-98\cdot99\cdot100+99\cdot100\cdot101\)

\(\Leftrightarrow3\cdot A=99\cdot100\cdot101\)

\(\Leftrightarrow A=33\cdot100\cdot101=333300\)

b) Ta có: \(1+2-3-4+...+97+98-99-100\)

\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(97+98-99-100\right)\)

\(=\left(-4\right)+\left(-4\right)+...+\left(-4\right)\)

\(=-4\cdot25=-100\)

! là j z

\("!"\)  là giai thừa đó bạn ạ .

\(VD:\)  \(3!=1.2.3=6\)

          \(4!=1.2.3.4=24\)

Ta có a=1.2+2.3+3.4+...+99.100  

         b=1²+2²+3²+...+99²=1.1+2.2+3.3+4.4+...+99.99

         a-b=(1.2+2.3+3.4+...+99.100)-(1.1+2.2+3.3+...+99.99)=(1.2-1.1)+(2.3-2.2)+(3.4-3.3)+(99.100-99.99)

             =1+2+3+...+99

             =(99+1)+(98+2)+(97+3)+...+(49+51)+50

             =100.49+50

             =4950

cảm ơn bạn nhiều

a) 1+2+3+...+100

Số số hạng của dãy là:

(100-1):1+1=100 (số)

Tổng của dãy số trên là:

(100+1).100:2=5050

b) 1+3+5+7+..+99

Số số hạng của dãy trên là:

(99-1):2+1=50(số)

tổng của dãy số trên là:

(99+1).50:2=2500

câu c) mk nghĩ nhân 3 lên

cảm ơn nha     ^-^!!!

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.......\frac{99^2}{99.100}.\frac{100^2}{100.101}\)

\(=\frac{1.2.3.....100}{1.2.3....100}.\frac{1.2.3....100}{2.3.4...101}\)

\(=1.\frac{1}{101}=\frac{1}{101}\)

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{99^2}{99.100}.\frac{100^2}{100.101}\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{99}{100}.\frac{100}{101}\)

\(=\frac{1.2.3...99.100}{2.3.4...100.101}\)

\(=\frac{1}{101}\)

\(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+99\cdot100\cdot101-98\cdot99\cdot100\)

\(3A=99\cdot100\cdot101\Rightarrow A=\dfrac{99\cdot100\cdot101}{3}=333300\)

\(B=1^2+2^2+3^2+...+99^2+100^2\)

\(=\dfrac{100\cdot\left(100+1\right)\cdot\left(2\cdot100+1\right)}{6}\)

\(=\dfrac{2030100}{6}=338350\)

\(C=1\cdot2\cdot3+2\cdot3\cdot4+...+8\cdot9\cdot10\)

\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+8\cdot9\cdot10\cdot\left(11-7\right)\)

\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+8\cdot9\cdot10\cdot11-7\cdot8\cdot9\cdot10\)

\(4C=8\cdot9\cdot10\cdot11\Rightarrow C=\dfrac{8\cdot9\cdot10\cdot11}{4}=1980\)

@Hồng Phúc Nguyễn

A = 1 . 2 + 2 . 3 + 3 . 4 + 99 . 100

3A = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 99 . 100 . (101 - 98)

3A = 1 . 2 . 3 + 2 . 3 . 4 - 2 . 3 . 1 + 3 . 4 . 5 - 3 . 4 . 2 + ... + 99 . 100 . 101 - 99 . 100 . 98

3A = 99 . 100 . 98

A = 33 . 100 . 98

A = 323400