Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

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

$${thanks}\:{so}\:{much}\:{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com