Question

a)  

\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+…..\(\frac{1}{1999.2000}\) 

Answer 1

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1999.2000}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1999}-\frac{1}{2000}\)

\(=1-\frac{1}{2000}\)

\(=\frac{1999}{2000}\)

Answer 2

1/1.2+1/2.3+1/3.4+..+1/1999.2000

=1-1/2+1/2-1/3+1/3-1/4+....+1/999-1/2000

=1-1/2000

Answer 3

a) \(\frac{1}{1.2}\)\(+\)\(\frac{1}{2.3}\)\(+\)\(\frac{1}{3.4}\)\(+...+\)\(\frac{1}{1999.2000}\)

\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{2}\)\(+\)\(\frac{1}{2}\)\(-\)\(\frac{1}{3}\)\(+\)\(\frac{1}{3}\)\(-\)\(\frac{1}{4}\)\(+\)\(...+\)\(\frac{1}{1999}\)\(-\)\(\frac{1}{2000}\)

\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{2000}\)

\(=\)\(\frac{1999}{2000}\)