Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

60, -10, 5/3, -5/18


Diverges


Converges; 11100 (this is definitely the wrong answer.)


Converges; 72


Converges; 0

Answer 1

Converges; 51 3/7

Explanation:

The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.

Then the sum of the sequence is given by ...

S = a1/(1 -r) = 60/(1 -(-1/6))

S = 60/(7/6) = 360/7

S = 51 3/7

_____

If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.