Question

1/1x2+1/2x3+1/3x4+...+1/999x1000+1

Answer 1

1 và 999/1000

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.100}+1\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{100}\)+1

=\(1-\frac{1}{100}\)+1

=\(\frac{99}{100}+1\)

=\(\frac{199}{100}\)

Answer 3

sorry mk lộn bài này mới đúng :

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)+1

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}+1\)

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

=\(\frac{999}{1000}+1\)

=\(\frac{1999}{1000}\)