Homework 11.6: pp 761--, #26, 30, 40

#26:

(∑_(n=1)^Infinity)2^(n^2)/n!

#30 -- notice the unusual capital Greek letter “Pi”: it means to multiply the elements of the sequence.

L=(∑_(n=1)^Infinity)(-2)^n*n!/(∏_(k=1)^n)(3k+2)
N[L]

#40

a[n_]:=n/2^n
S[j_]:=(∑_(n=1)^j)a[n]
N[S[10]]
r[n_]:=a[n+1]/a[n]
r[n]
L=Limit[r[n],n->Infinity]
Simplify[r'[n]]
ListPlot[r[Range[10]]]
N[a[11]/(1-L)]