Math not being my strong point, can someone tell me if the following sequence is convergent or divergent?
1-(3/2)+(9/4)-(27/8)+…
Thanks!
- That’s really more of series than a sequence, and
- It’s divergent.
What you have there is an example of a geometric series, which is something of the form:
1 + r + r[sup]2[/sup] + r[sup]3[/sup] + ···
In this case, r=-3/2. Geometric series converge (with a sum of 1/(1-r)) if |r| < 1, and diverge otherwise.
Another simple test for series in general (known as the Divergence test) is that if the terms don’t go to 0, the series diverges. In this case, the terms don’t go to 0. Hope that helps!