Question

If sn =1+1/3+1/3^2 +... +1/3^n prove that {sn} convergers

Answer 1

Let sn=1+1/2+1/3+...+1/nsn=1+1/2+1/3+...+1/n. why is this sequence convergent? Isn't it decreasing and it has a lower bound 0. Shouldn't a decreasing sequence, which is bounded below be convergent?