Math Help - Sequence question, is this correct?

1. Sequence question, is this correct?

hi everyone

Question

a)Calculate the following sequence:
{(n^3)/(n^3+n^2+1)}^5,n=0

this is how i did it...
n = 1, =1/3
n=2,=8/13
n=3,27/37
n=4,64/81
n=5, 125/151

ans: 1/3,8/13,27/37,64/81,125/151

b){an}^6 ,n=0 if a(n+1)= (an+3)/(an+1), a0=2

a1= (2+3)/(2+1) = 5/3
a2=(3+3)/(3+1)=3/2
a3=(4+3)/(4+1)=7/5
a4=(5+3)/(5+1)=8/6
a5=(6+3)/(6+1)=9/7
a6=(7+3)/(7+1)=10/8

ans:5/3,3/2,7/5,4/3,9/7,5/4

2. Originally Posted by anderson
hi everyone

Question

a)Calculate the following sequence:
{(n^3)/(n^3+n^2+1)}^5,n=0

this is how i did it...
n = 1, =1/3
n=2,=8/13
n=3,27/37
n=4,64/81
n=5, 125/151

ans: 1/3,8/13,27/37,64/81,125/151

b){an}^6 ,n=0 if a(n+1)= (an+3)/(an+1), a0=2

a1= (2+3)/(2+1) = 5/3
a2=(3+3)/(3+1)=3/2
a3=(4+3)/(4+1)=7/5
a4=(5+3)/(5+1)=8/6
a5=(6+3)/(6+1)=9/7
a6=(7+3)/(7+1)=10/8

ans:5/3,3/2,7/5,4/3,9/7,5/4

The first problem Looks good. Iexamined your method, but did not check every part of your arithmitic, so double check what you have done. Again, your method is correct.

But, wait. In the secendon problem, $a_2=\frac{\frac{5}{3}+3}{\frac{5}{3}+1}$ .

$a_3=\frac{a_2+3}{a_2+1}\mbox{ and }a_4=\frac{a_3+3}{a_3+1}\mbox{ and }a_5=\frac{a_4+3}{a_4+1}\mbox{ and etc...}$

3. question b is
{ $a_n$} $^{6}_{n=0}$ if $a_{n+1}$ = ( $a_n$+3)/( $a_n$+1)

is my answer correct, your working is slightly different.thank you for help & guidance.