Prove the following by using the principle of mathematical induction for all n ∈ N:
`1+ 1/((1+2)) + 1/((1+2+3)) +...+ 1/((1+2+3+...n)) = (2n)/(n +1)`
Thus, P(k + 1) is true whenever P(k) is true.
Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.
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- Principle of Mathematical Induction
Solution Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: `1+ 1/((1+2)) + 1/((1+2+3)) +...+ 1/((1+2+3+...N)) = (2n)/(N +1)` Concept: Principle of Mathematical Induction.