As per the inquiry,
![\[\Rightarrow P\left( k+1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0d17e4216b59f77dd0be0d0245938e26_l3.png "Rendered by QuickLaTeX.com")
is valid when P(k) is valid.
Along these lines, by Mathematical Induction,
![\[\surd n\text{ }<\text{ }1/\surd 1\text{ }+\text{ }1/\surd 2\text{ }+\text{ }\ldots \text{ }1/\surd n\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d7aeddccacc2995555af448c7064bd43_l3.png "Rendered by QuickLaTeX.com")
, for all normal numbers
![\[n\text{ }\ge \text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f4cc67cbaa127d3d7c2abccf7acd0f3b_l3.png "Rendered by QuickLaTeX.com")
As per the inquiry,
is valid when P(k) is valid.
Along these lines, by Mathematical Induction,
, for all normal numbers
