Question

P=1/1.2.3+1/2.3.4+1/3.4.5+...+1/10.11.12

Answer 1

2P=2/1.2.3+2/2.3.4+2/3.4.5+2/10.11.12
2P=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+.....+1/10.11-1/11.12
2P=1/1.2-1/11.12
2P=1/2-1/132
2P=66/132-1/132
2P=65/132
 P=65/264

Answer 2

\(P=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{10.11.12}\)

\(P=\dfrac{1}{2}-\dfrac{1}{11.12}\)

\(P=\dfrac{65}{132}\)