Induction Question (2 Viewers)

Shuuya · Feb 25, 2016

Prove by using mathematical induction that:
$\\ \quad \\ a\quad +\quad ar\quad +\quad a{ r }^{ 2 }\quad +\quad ...\quad +a{ r }^{ n }\quad =\quad \frac { a({ r }^{ n+1 }-1) }{ r-1 }$

Help please :'(

davidgoes4wce · Feb 25, 2016

Shuuya said:
Prove by using mathematical induction that:
$\\ \quad \\ a\quad +\quad ar\quad +\quad a{ r }^{ 2 }\quad +\quad ...\quad +a{ r }^{ n }\quad =\quad \frac { a({ r }^{ n+1 }-1) }{ r-1 }$

Help please :'(

There are many different ways of doing induction but this is my method. It took 2 pages to do . (if someone sees something wrong let me know):

Shuuya · Feb 25, 2016

davidgoes4wce said:
There are many different ways of doing induction but this is my method. It took 2 pages to do . (if someone sees something wrong let me know):

Thank you!

I usually start with proving for n=1, but that wasn't working for some reason :/

InteGrand · Feb 25, 2016

Shuuya said:
Thank you! I usually start with proving for n=1, but that wasn't working for some reason :/

$\noindent If you started at $n=1$, the sum would be $a+ar$ (since it ends at $ar^n$, which is $ar$ when $n=1$). Were you just doing $a$?$

Shuuya · Feb 25, 2016

InteGrand said:
$\noindent If you started at $n=1$, the sum would be $a+ar$ (since it ends at $ar^n$, which is $ar$ when $n=1$). Were you just doing $a$?$

I forgot about 'a' so I only had 'ar'

Induction Question (2 Viewers)

Shuuya

Well-Known Member

davidgoes4wce

Well-Known Member

Shuuya

Well-Known Member

InteGrand

Well-Known Member

Shuuya

Well-Known Member

Users Who Are Viewing This Thread (Users: 0, Guests: 2)