Question

A=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{49\cdot50}\)

Answer 1

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}\)

\(A=\frac{49}{50}\)

Answer 2

A=1/1.2+1/2.3+...+1/49.50

  =1-1/2+1/2-1/3+...+1/49-1/50

  =1-1/50

  =49/50

Answer 3

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(\Rightarrow A=\frac{49}{50}\)

Answer 4

A=\(\frac{49}{50}\)

Answer 5

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{49.50}\)

A=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{49}-\frac{1}{50}\)

A=\(\frac{1}{1}-\frac{1}{50}\)

A=\(\frac{50}{50}-\frac{1}{50}\)

A=\(\frac{49}{50}\)

Answer 6

A=\(\frac{49}{50}\)

Answer 7

A=\(\frac{49}{50}\)

Answer 8

A=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+.......+\(\frac{1}{49.50}\)=

=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+........+\(\frac{1}{49}\)-\(\frac{1}{50}\)

=1-\(\frac{1}{50}\)

=\(\frac{49}{50}\)

Answer 9

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

A=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

A=\(\frac{1}{1}-\frac{1}{50}\)

A=\(\frac{50}{50}-\frac{1}{50}\)

A=\(\frac{49}{50}\)