Question

Consider the sequence: -2/3, 2/9, -2/27, 2/81, -2/243……

Part 1: A Formula 

Find a formula for the n^th term of this sequence:

a_n = _______ ∑

Part 2: Limit of the Sequence 

Find the limit of the sequence: 

lim(n->∞) a_n = _______ ∑

Remember: INF, -INF, DNE are also possible answers. 

Part 3: 

Converge or Diverge? 

Does this sequence converge or diverge?

Answer 1

Geometric series test:- If a series of the form

if |r|<1 then series converges and sum is S= a/(1-r)

if |r|>1 then series diverges

Here a=-2/3 ; r=-1/3

|r|=1/3<1

so series converges

Sum