求一些級數的斂散性[微積分]

Q1.
a(k)=(k+1)/[(k+2)(k+3)]>0
lim(k->inf) a(k)/ (1/k)=lim(k->inf) k(k+1)/[(k+2)(k+3)]=1
by limit comparison test and Σ(1/k) div.
so Σ (k+1)/[(k+2)(k+3)] div

Q2.
a(n)=2^(1/n)-1>0
lim(n->inf) a(n)/(1/n)=lim(x->0) (2^x -1)/x =(L' rule) lim(x->0) 2^x*ln(2)=ln(2)
by limit comparison test and Σ(1/n) div
so Σ[2^(1/n)-1] div.