Question

For each of the sequences below, decide whether it converges and, if it does, state its limit. Justify your answers briefly.
(i) an =6n^4 +2n^3/7n− 11n^4 (n =1,2,3,...)
(ii) bn =3 − 3^n/7(0.9)^n + 8 (n=1,2,3,...)

Answer 1

i) lim (n- infinity) use L'hospiTAL'S Rule 3 time (you have indeterminate form of type infinity/infinity) after simplifying = -36/66=-6/11
ii) to find a lim - use Ratio Test a(n+1)/a(n)=....3