Does the series 1/(1+(2/3)^n) converge or diverge?

converge-or-diverge

#1

Does the series 1/(1+(2/3)^n) converge or diverge?

Answer:

It will diverge. The best way for me to remember the difference is that “di-” means two and two is more than one. The key part of this to look at is the part being raised to the power (in this case it is 2/3). Since 2/3 is less than one, the number will be getting smaller. HOWEVER, this isn’t true in this instance because it is on the bottom of the fraction, the value of this number is inversely related to the term in the sequence. So the sum gets larger and larger as you go so it diverges