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Question Number 64812 by Rio Michael last updated on 21/Jul/19
how do i prove by induction?  please
$${how}\:{do}\:{i}\:{prove}\:{by}\:{induction}? \\ $$$${please} \\ $$
Commented by MJS last updated on 21/Jul/19
show that it′s true for n_0 ∈N  usually for n_0 =0 or n_0 =1 but any n_0 ∈N will do    show that if it′s true for n ⇒ it′s true for n+1    ⇒ it′s true for all n∈N with n≥n_0
$$\mathrm{show}\:\mathrm{that}\:\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:{n}_{\mathrm{0}} \in\mathbb{N} \\ $$$$\mathrm{usually}\:\mathrm{for}\:{n}_{\mathrm{0}} =\mathrm{0}\:\mathrm{or}\:{n}_{\mathrm{0}} =\mathrm{1}\:\mathrm{but}\:\mathrm{any}\:{n}_{\mathrm{0}} \in\mathbb{N}\:\mathrm{will}\:\mathrm{do} \\ $$$$ \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:{n}\:\Rightarrow\:\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:{n}+\mathrm{1} \\ $$$$ \\ $$$$\Rightarrow\:\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:{n}\in\mathbb{N}\:\mathrm{with}\:{n}\geqslant{n}_{\mathrm{0}} \\ $$
Commented by Rio Michael last updated on 22/Jul/19
thanks so much sir
$${thanks}\:{so}\:{much}\:{sir} \\ $$

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