Recall that for 1 x 1 the Taylor expansion for f x a lim 1 1 c which is also known as a geometric series Use this result to calculate the following limits b 11 400 1 1 1 3 3 3 3 4 8 3 16 32 64 9 27 81 1 1 z 1 3 n centred at z 0 is given by 1 x x x x Note Both of these objects are generally referred to as infinite sums or series The first expression explicitly gives the nth term and asks you to calculate the limit as noo whereas the second implicitly suggests via the that what you are calculating is an infinite sum of terms Althoug they look different they are asking for the same thing for you to calculate the sum of all their infinite terms