# Exercici 05.7

kill(all)$

a[k]:=k;  
num1[n]:=product(a[k], k, 1, n);
makelist(num1[n], n, 1, 10);

b[k]:=2*k+1;  
den1[n]:=product(b[k], k, 1, n);
makelist(den1[n], n, 1, 10);

c[n]:=((-1)^(n+1))*((num1[n])/(den1[n]))*(2^n);
makelist(c[n], n, 1, 10);
makelist(c[n], n, 1, 10), numer;

A[m]:=sum(c[n], n, 1, m);
makelist(A[m], m, 1, 10);

makelist(A[2*m], m, 1, 10);
makelist(A[2*m], m, 1, 10), numer;

makelist(A[2*m-1], m, 1, 10);
makelist(A[2*m-1], m, 1, 10), numer;

A[100], numer;  A[101], numer;

A[1000], numer;  A[1001], numer;

A[1020], numer;  A[1021], numer;

Per tant, la suma de la sèrie es troba a l'interval ]0.36, 0.40[.