Prove by mathematical induction that 1/1x2 + 1/2x3 + 1/3x4 + ... 1/n(n+1) = n/n+1

Question

step by step answers please

Answer 1

1.

Demonstrate true for n = 1

1 / (1(1 + 1) = 1 / (n + 1)

1 / 2 = 1 / 2

2.

Assume true for "n"

1 / (n(n + 1) = n / (n + 1)

3.

Demonstrate true for "n + 1"

[1 / (n(n + 1)] + [1 / (n + 1)(n + 1 + 1)] = [n / (n + 1)] + [1 / (n + 1)(n + 1 + 1)]

Simplifying the right side

[n / (n + 1)] + [1 / (n + 1)(n + 1 + 1)]

[n / (n + 1)] + [1 / (n + 1)(n + 2)]

[n(n + 2) + 1] / (n + 1)(n + 1 + 1)]

[n² + 2n + 1] / (n + 1)(n + 1 + 1)

(n + 1)² / (n + 1)(n + 1 + 1)

(n + 1) / (n + 1) + 1

QED