Problem $1$: For each power series, state its center, the interval of convergence, and the radius of convergence.

a$.\backslash$sum$\_($n$=1)^(\backslash$infty $)(-1)^($n$)($x$^(2$n$+1))/(2^($n$)$n$)$

e$.\backslash$sum$\_($n$=1)^(\backslash$infty $)($x$^($n$))/($n$-4$lnn$)$

b$.\backslash$sum$\_($n$=0)^(\backslash$infty $)(8^($n$))/($n$!)(2$x$-1)^($n$)$

f$.\backslash$sum$\_($n$=1)^(\backslash$infty $)(2^($n$))/(3$n$)(3$x$+2)^($n$)$

c$.\backslash$sum$\_($n$=0)^(\backslash$infty $)(4^($n$))/((2$n$+1)!)$x$^(2$n$-1)$

g$.\backslash$sum$\_($n$=0)^(\backslash$infty $)27^($n$)($x$-1)^(3$n$+2)$

d$.\backslash$sum$\_($n$=0)^(\backslash$infty $)((-1)^($n$)$x$^($n$))/(\backslash$sqrt$($n$^(2)+1))$

h$.\backslash$sum$\_($n$=12)^(\backslash$infty $)$ e$^($n$)($x$-2)^($n$)$

Could you please do every problem?