SOLUTION: Induction Sum: Prove using mathematical induction that: 1/1*2*3 + 1/2*3*4 + 1/3*4*5 +...+ 1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2)

SOLUTION: Induction Sum: Prove using mathematical induction that: 1/123 + 1/234 + 1/345 +...+ 1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2)

Question 1183960: Induction Sum:
Prove using mathematical induction that:
1/1*2*3 + 1/2*3*4 + 1/3*4*5 +...+ 1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Step 1. For n = 1, , and the statement is true.

Step 2. (Inductive Hypothesis) Let statement be true for n = k for some positive integer k, that is,

Step 3. Prove statement for n = k+1: .

=

=

Hence the staement is true for n = k+1. Therefore the staement is true for .
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