help me how to define themQuote:

give a recursive definaition of the sequence {$\displaystyle {a_n}$} , n=1,2,3,...

a) $\displaystyle a_n = 1+(-1)^n$

b) $\displaystyle a_n = n(n+1)$

c) $\displaystyle a_n = n^2$

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- Oct 24th 2009, 01:56 PMzpwncheninduction and recursionQuote:

give a recursive definaition of the sequence {$\displaystyle {a_n}$} , n=1,2,3,...

a) $\displaystyle a_n = 1+(-1)^n$

b) $\displaystyle a_n = n(n+1)$

c) $\displaystyle a_n = n^2$

- Oct 24th 2009, 02:47 PMproscientia
**(a)**

The sequence alternates between $\displaystyle 0$ and $\displaystyle 2$ starting with $\displaystyle 0.$ The sum of two consecutive terms is $\displaystyle 2.$ Hence

$\displaystyle a_1=0,\quad a_{n+1}=2-a_n$

**(b)**

$\displaystyle a_1=2,\quad a_{n+1}=(n+1)(n+2)=n(n+1)\frac{n+2}n=a_n\frac{n+2} n$

**(c)**

I leave this one to you. - Oct 24th 2009, 08:50 PMzpwnchen
c) $\displaystyle a_n = a_n +2(n+1) -1 ,a_1=1$ is that correct?

- Oct 25th 2009, 12:04 AMCaptainBlack
- Oct 25th 2009, 12:08 AMCaptainBlack
See here

CB