Question

1/1.2 + 1/2.3 + ... +1/x(x+1)

Answer 1

1/1.2 + 1/2.3 + ... + 1/x(x + 1)

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/x - 1/x + 1

= 1 - (1/2 - 1/2) - (1/3 - 1/3) - ... - (1/x - 1/x) - 1/x + 1

= 1 - 1/x + 1

= x / x + 1

Answer 2

1/1.2 + 1/2.3 + ... + 1/x(x + 1)

= 1 - 1/2 + 1/2 - 1/3 + ... + 1/x - 1/x + 1

= 1 - 1/x + 1

= x/x + 1