Question

How do you find the first five terms given `a_1=3/4`, `a_(n+1)=(n^2+1)/n*a_n`?

Answer 1

Sequence is `{3/4,3/2,15/4,25/2,425/8,............}`

Explanation:

As `a_1=3/4`

`a_2=a_(1+1)=(1^2+1)/1*a_1=2*3/4=3/2`

`a_3=a_(2+1)=(2^2+1)/2*a_2=5/2*3/2=15/4`

`a_4=a_(3+1)=(3^2+1)/3*a_3=10/3*15/4=25/2`

`a_5=a_(4+1)=(4^2+1)/4*a_3=17/4*25/2=425/8`

and sequence is `{3/4,3/2,15/4,25/2,425/8,............}`