Question

Tính tổng sau :

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...........+\frac{1}{999\cdot1000}+1\)

Dấu chấm ở trên là dấu nhân

 

Answer 1

1/1x2+1/2x3+1/3x4+...+1/99x100+1

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

=1- 1/100 +1

=99/100 +1

=199/100

Answer 2

1/1.2 + 1/2.3 + 1/3.4 + ... + 1/999.1000 + 1

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/999 - 1/1000 + 1

= 1 - 1/1000 + 1

= 2 - 1/1000

= 2000/1000 - 1/1000

= 1999/1000

Ủng hộ mk nha ♡_♡☆_☆

Answer 3

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{999}-\frac{1}{1000}\)+1

\(=1-\frac{1}{1000}+1\)

=1-1+1/1000

= 1/1000

Answer 4

A = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/999.1000 + 1

Đặt A = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/999.1000 + 1

A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/999 - 1/1000 + 1

A = 1/1 - 1/1000 + 1

A = 999/1000 + 1

A = 1999/1000

 Vậy A = 1999/1000

Answer 5

nhầm = 1999/1000