Question

Determine whether the sequence a_n= (n+1)^1/2 divided by 5n+3 is increasing or decreasing.

Answer 1

\[a _{n+1}-a _{n}=[(n+2)^{1/2}/5(n+1)+3]-[(n+1)^{1/2}/5n+3]\]
if greater or equao to 0 increasing but if <0 decreasing

Answer 2

\[\LARGE a_8=\frac{\sqrt{8+1}}{5\cdot 8+3}=\frac{3}{43}\] if
\[\LARGE a_9=\frac{\sqrt{9+1}}{5\cdot 9+3}=\frac{\sqrt{10}}{48}\] ... simple example, go on , and substitute, you'll see how it goes !

Answer 3

Thanks guys.