Question

Bai 1: Tinh :

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

B = 1.2+2.3+3.4+4.5+...+99.100

Answer 1

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

A = ( 1 - 2 ) + ( 2 - 3 ) + ....+ ( 99 - 100 )

A = ( - 1 ) + ( - 1 ) +....+ ( - 1 )

A = ( - 1 ) . 50

A = - 50

B = 1.2 + 2.3 + 3.4 + 4.5 +...+ 99.100 
Nhân cả 2 vế với 3, ta được: 
3A=1.2.3+ 2.3.3+ 3.4.3+ 4.5.3+...... 99.100.3 
= 1.2.3 + 2.3(4-1) + 3.4.(5-2) +...+ 99.100.(101-98) 
= 1.2.3 + 2.3.4 -1.2.3 + 3.4.5-2.3.4 +...+ 99.100.101-98.99.100 
= 99.100.101 
=) B = (99.100.101) :3 
B = 333300  
Vậy  B= 333300 

 

Answer 2

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

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

A = (-1) + (-1) + (-1) + ...+ (-1)

A = (-1).50

A = 1

Answer 3

B = 1.2+2.3+3.4+4.5+...+99.100

3B = 1.2.3 +2.3.3+ 3.4.3+...+99.100.3 
3B = 1.2.3 +2.3(4-1)+ 3.4(5-2)+...+99.100(101-98) 
3B = 1.2.3 +2.3.4-1.2.3+ 3.4.5-2.3.4+...+99.100.101-98.99.100 
3B = 99.100.101

3B = 999900 
B = 999900 : 3

B = 333300

Answer 4

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

\(A=\left(1-2\right)+\left(3-4\right)+\left(4-5\right)+...+\left(99-100\right)\) ( 50 cặp số )

\(A=-1+\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\) ( 50 số -1 )

\(A=-1.50=-50\)

Vậy A = - 50