$(4$ pts$)6\backslash$sum$\_($n$=1)^(\backslash$infty $)(4^($n$))/(2^($n$)+5^($n$))$ converges or diverges. Compare $\backslash$sum$\_($n$=1)^(\backslash$infty $)(4^($n$))/(2^($n$)+5^($n$))$ to $\backslash$sum$\_($n$=1)^(\backslash$infty $)(4^($n$))/(2^($n$))\backslash$sum$\_($n$=1)^(\backslash$infty $)(4^($n$))/(2^($n$))=\backslash$sum$\_($n$=1)^(\backslash$infty $)2^($n$)$ which is a geometric series with r$=2$ Since $|$r$|=2>1,\backslash$sum$\_($n$=1)^(\backslash$infty $)2^($n$)$ diverges and thus $\backslash$sum$\_($n$=1)^(\backslash$infty $)(4^($n$))/(2^($n$)+5^($n$))$ also diverges by Comparison Test