a)Ta có:

 A= 1/1.2+1/2.3+1/3.4+.....+1/99.100

=1-1/2+1/2-1/3+...+1/99-1/100

=1-1/100

=99/100

b)Ta có:

B= 1/11+1/12+1/13+1/14+1/15+...+1/50

=(1/11+1/50)+(1/12+1/49)+...+(1/30+1/31)

=61/11.50+61/12.49+...+61/30.31

=61.(1/11.50+1/12.49+...+1/30.31)

Mình xin lỗi chỉ làm được đến đây vì dạng tính B mình không tốt lắm ◕◡◕

\(B=\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{30}\right)+\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{50}\right)>\left(\frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}\right)+\left(\frac{1}{50}+\frac{1}{50}+...+\frac{1}{50}\right)\)=> \(B>\frac{20}{30}+\frac{20}{50}=\frac{2}{3}+\frac{2}{5}=\frac{16}{15}>1\)

mà \(A=\frac{99}{100}

ssssssssss

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

\(a,A=1\cdot2+2\cdot3+...+98\cdot99\\ 3A=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+98\cdot99\cdot3\\ 3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\left(5-2\right)+...+98\cdot99\left(100-97\right)\\ 3A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+3\cdot4\cdot5-...-97\cdot98\cdot99+98\cdot99\cdot100\\ 3A=98\cdot99\cdot100=970200\\ A=323400\)

\(b,B=1^2+2^2+3^3+...+98^2\\ B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+98\left(99-1\right)\\ B=\left(1\cdot2+2\cdot3+3\cdot4+...+98\cdot99\right)-\left(1+2+...+98\right)\\ B=323400-\left[\left(98+1\right)\left(98-1+1\right):2\right]\\ B=323400-4851=318549\\ c,C=1\cdot99+2\left(99-1\right)+3\left(99-2\right)+...+98\left(99-97\right)+99\left(99-98\right)\\ C=1\cdot99+2\cdot99-1\cdot2+3\cdot99-2\cdot3+...+98\cdot99-97\cdot98+99\cdot99-98\cdot99\\ C=99\left(1+2+...+99\right)-\left(1\cdot2+2\cdot3+...+98\cdot99\right)\\ C=99\left[\left(99+1\right)\left(99-1+1\right):2\right]-323400\\ C=490050-323400=166650\)

https://hoc24.vn/cau-hoi/a-tinh-tong-a1223349899b-su-dung-ket-qua-cau-a-tinh-b122232972982c-su-dung-ket-qua-cau-a-tinh-c1992983979829.2030286199021

:vv hỏi hoài z?

Mình làm mẫu 1 bài nha !

Có : 12A = 1.5.12+5.9.12+....+101.105.12

= 1.5.12+5.9.(13-1)+.....+101.105.(109-97)

= 1.5.12+5.9.13-1.5.9+.....+101.105.109-97.101.105

= 1.5.12-1.5.9+101.105.109

= 1155960

=> A = 1155960 : 12 = 96330

Tk mk nha

Có : 4D = 1.2.3.4+2.3.4.4+....+98.99.100.4

= 1.2.3.4+2.3.4.(5-1)+.....+98.99.100.(101-97)

= 1.2.3.4+2.3.4.5-1.2.3.4+......+98.99.100.101-97.98.99.100

= 98.99.100.101

=> D = 98.99.100.101/4 = 24497550

a ta co ;

13 -12 +11+10-9+8-7-6+5-4+3+2-1

=13-(12-11-10+9) +(8-7-6+5) -(4-3-2+1)

= 13 -0+0 -0

=13

câu a = 13 còn câu b thì để tuần sau nhé

13-12+11+10-9+8-7-6+5-4+3+2-1

=11+11+10-9+8-7-6+5-4+3+2-1

=    22  +  1  + 1  - 11  - 7  + 1

=          23     +1  -11-7+1

=                24 -11-7+1

=                    13-8

=                        5