# Ejercicio 05.3

## Apartado a)

kill(all)$

x1=x1:(-2)/7.25;
x2=x2: 4/7.25;

S1=S1: x1/(1-x1);
S2=S2: x2/(1-x2);

Suma=S1+S2;

## Apartado b)

kill(all)$

x[n]: 2.32/(2.43*n^2 + 2.43*n);

R1=R1: x[n] ;

partfrac(R1, n);

b[n]:= 232/(243*n) ;

sum(x[n], n, 1, inf) = b[1] - limit(b[n], n, inf);

## Apartado c)

kill(all)$

x[n]:=(3.25*n)/((n+1)!);

S=sum(x[n], n, 1, inf);

b[n]:= n/(n+1)! ;

c[n] := 1/(n!);

c[n] - c[n+1];

ratsimp(%);

S= 3.25 * ( (%e-1) - (%e -1 -1));

S[m]:=sum(x[n], n, 1, m);

S[20];

S[40];