Question

Tính các tổng sau :

a 2+4+6+...+1998+2000 = ?

b 5+9+13+...+1997+2001 = ?

c 1.2+2.3+3.4+4.5+5.6+...+99.100 [ Dấu . là dấu nhân ]

 

Answer 1

TL:

a)\(2+4+6+...+2000=\frac{\left(2+2000\right).\left[\left(2000-2\right):2+1\right]}{2}\) 

\(=1001000\)

Câu b tương tự nha bạn:)

c) Đặt 1.2+2.3+....+99.100 =A

\(3A=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\) 

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

\(3A=99.100.101\) 

\(A=333300\) 

Vậy .....

Answer 2

a) Đặt A= 2+4+6+...+1998+2000 

Ta có: A=(2+2000).1000:2

=> A=2002.1000:2

=> A=2002000:2

=> A=1001000

b) Đặt B= 5+9+13+...+1997+2001 

=> B=(2001+5).500:2

=> B=2006.500:2

=> B=1003000:2

=> B=501500

c)Đặt S= 1.2 + 2.3 + 3.4 + ...+ 99.100
=> 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101 => 3S = 3.33.100.101 
=> S=33.100.101= 333300

Answer 3

a) 2+4+6+...+1998+2000 

=(2+2000).1000:2

=2002.1000:2

=1001000

b) 5+9+13+...+1997+2001 

=(2001+5).500:2

=2006.500:2

=501500

c)đặt A=1.2 + 2.3 + 3.4 + ...+ 99.100
=> 3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3A= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3A = 99.100.101 
=> A=33.100.101= 333300