Question

tính nhanh

Z=1.2+2.3+3.4+...........+99.100

Answer 1

3Z = 1.2.3 + 2.3.3 + 3.3.4 + .... + 3.99.100 
 Z= 1.2.3 + 2.3.4 + 3.4.5 + .... + 99.100.101 
=> Z - 3Z = 1.2.3 - 1.2.3 + 2.3.(4-3) + 3.4 ( 5-3) + .... + 99.100 ( 101 -3) 
= 1.2.3 + 2.3.4 + .... + 98.99.100 
=> Z -3Z = Z - 99.100.101 
=> Z  = 99.100.101/3 = 333300

Answer 2

\(Z=1.2+2.3+3.4+...+99.100\)

\(3Z=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)

\(3Z=1.2.3+2.3.4-1.2.3+3.4.5-2.4.5+...+99.100.101-98.99.100\)

\(3Z=99.100.101\)

\(Z=\frac{99.100.101}{3}=\frac{999900}{3}=333300\)

Answer 3

Z = 1.2 + 2.3 + 3.4 + ......... + 99.100

1/Z = 1/1.2 + 1/2.3 + 1/3.4 + .......... + 1/99.100

1/Z = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ..... + 1/99 - 1/100

1/Z = 1/1 - 1/100

1/Z = 1/1 - 1/100

1/Z = 99/100

Z = 100/99