Ta có:
A=1.3.5+3.5.7+5.7.9+...................+2015.2017.2019

8A=1.3.5.8+3.5.7.8+5.7.9.8+.......................+2015.2017.2019.8

8A=1.3.5.(7+1)+3.5.7.(9-1)+5.7.9.(11-3)+......................+2015.2017+2019.(2021-2013)

8A=1.3.5.7+15+3.5.7.9-1.3.5.7+5.7.9.11-3.5.7.9+.........................+2015.2017.2019.2021-2013.2015.2017.2019

8A=15+2015.2017.2019.2021

A=(15+2015.2017.2019.2021)/8

t i c k cho mình nha mình suy nghĩ khá lâu đấy

tôi giải lâu rồi

1.3.5+3.5.7+5.7.9+...+97.99.101

=(101-2).(101-1).101.(101+1):4

=25497450

1/1.3.5 + 1/3.5.7 + 1/5.7.9 +.....+ 1/99.101.103

= 1/4. [4/1.3.5 + 4/3.5.7 + 4/ 5.7.9 +....+ 4/99.101.103]

=1/4. [1/1.3 - 1/3.5 + 1/3.5 - 1/5.7 +....+ 1/99.101 - 1/101.103]

= 1/4. [1/1.3 - 1/101.103]

=1/4. 10406/31209

= 5230/62418

\(A=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+....+\frac{1}{99\cdot101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5-7}+....+\frac{1}{99\cdot101}-\frac{1}{101\cdot103}\)

\(2A=\frac{1}{1\cdot3}-\frac{1}{101\cdot103}\)

Tính nốt

\(G=1.3.5+3.5.7+5.7.9+...+95.97.99\)

\(G=1+99.\left(3+5+7+...+97\right)\)\

\(G=100.\left[\left(3+97\right)+\left(5+95\right)+...+\left(49+51\right)\right]\)

\(G=100.\left(100.24\right)\)

\(G=100.2400=240000\)

240000

1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)

= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99

= 15 + 95.97.99.101

=> \(A=\frac{15.95+97.99.101}{8}\)

Tách ra rồi tính

Bài này rất dễ may cho bạn là hôm nay minh rảnh nên mới giải cho tiết.Thôi tớ làm nhé!

Theo bài ra ta có :

A =1.3.5+3.5.7+5.7.9+...+97.99.101

8A=8.(1.3.5+3.5.7+5.7.9+...+97.99.101)

8A=1.3.5.8+3.5.7.8+5.7.9.8+...+97.99.101.8

8A=1.3.5.(7+1)+3.5.7(9-1)+5.7.9.(11-3)+...+97.99.101.(103-95)

8A=1.3.5.7+1.1.3.5+3.5.7.9-1.3.5.7+5.7.9.11-3.5.7.9+...+97.99.101.103-95.97.99.101

8A=1.1.3.5+97.99.101.103

8A=15+99900009

8A=99900024

A =99900024:8

A =12487503

Vậy A=12487503

 D = 4/1.3.5+4/3.5.7+4/5.7.9+4/7.9.11+4/9.11.13

D.\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)

D\(=\frac{1}{1.3}-\frac{1}{11.13}\)

D\(=\frac{1}{3}-\frac{1}{143}\Rightarrow D=\frac{140}{429}\)