Prove by method of induction, for all $n \in N$: $1.2 + 2.3 + 3.4 + \ldots + n(n+1) = \dfrac{n}{3}(n+1)(n+2)$.

Prove by method of induction, for all n ∈ N: 1.2 + 2.3 + 3.4 + … + n(n+1) = (n)/(3)(n+1)(n+2).

EXERCISE 4.1 · Q6

n \in N

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Let $P(n):1.2+2.3+\cdots+n(n+1)=\dfrac n3(n+1)(n+2)$ . Base: $n=1$ : L.H.S. $=2$ , R.H.S. $=\dfrac13(2)(3)=2$ ; holds. Hypothesis: assume true for $k$ . Step: add $(k+1)(k+2)$ : $\dfrac k3(k+1)(k+2)+(k+1)(k+2)=(k+1)(k+2)\left[\dfrac k3+1\right]=(k+1)(k+2)\cdot\dfrac{k+3}{3}=\dfrac{(k+1)}{3}(k+2)(k+3)$ , matc …

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Q.Prove by method of induction, for all $n \in N$ : $1.2 + 2.3 + 3.4 + \ldots + n(n+1) = \dfrac{n}{3}(n+1)(n+2)$ .

Concept understanding — Principle of Mathematical Induction

Q.Prove by method of induction, for all n∈Nn \in Nn∈N: 1.2+2.3+3.4+…+n(n+1)=n3(n+1)(n+2)1.2 + 2.3 + 3.4 + \ldots + n(n+1) = \dfrac{n}{3}(n+1)(n+2)1.2+2.3+3.4+…+n(n+1)=3n​(n+1)(n+2).

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Q.Prove by method of induction, for all $n \in N$ : $1.2 + 2.3 + 3.4 + \ldots + n(n+1) = \dfrac{n}{3}(n+1)(n+2)$ .

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