SOLUTION:-
![\[P\text{ }\left( k\text{ }+\text{ }1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b0c5cd070a4723f5916fc5a21e2c2d93_l3.png "Rendered by QuickLaTeX.com")
is valid at whatever point
![\[P\text{ }\left( k \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4b056dfe3552858b65eefbdf4d806d85_l3.png "Rendered by QuickLaTeX.com")
is valid.
Thus, by the rule of numerical enlistment, articulation
![\[P\text{ }\left( n \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8ba3815da790b3fb3750c2605ca0d157_l3.png "Rendered by QuickLaTeX.com")
is valid for all regular numbers for example
![\[n.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a9f886993539c0b1f9d4400f02cd127f_l3.png "Rendered by QuickLaTeX.com")
Prove the following by using the principle of mathematical induction for all n ∈ N:
Prove the following by using the principle of mathematical induction for all n ∈ N: