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Give an example of a statement P (n) such that it is true for all n ϵ N
Give an example of a statement P (n) such that it is true for all n ϵ N
CBSE | Class 11 | Exercise 12.1 | Mathematical Induction | Maths | RD Sharma
Give an example of a statement P (n) such that it is true for all n ϵ N

Let ,

\[P\text{ }\left( n \right)\text{ }=\text{ }1\text{ }+\text{ }2\text{ }+\text{ }3\text{ }+\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }+\text{ }n\text{ }=\text{ }n\left( n+1 \right)/2~\]

Hence,

P (n) is true for all natural numbers.

Hence, P (n) is true for all n ∈ N.

 

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