Which of the following series diverges?
a) 5 + 10 + 15 + 20 +...
b) 45 + 15 + 5 + 5/3 + ...
c) 3/4 + 3/16 + 3/64 +..
d) 1/2 + 1/4 + 1/8 + 1/16 +...
Thank you!
Probably a) because you can see that the numbers are getting bigger, and will reach infinity without stopping.
The other ones are getting smaller, so at some point, they'll reach a definite number, or really close to one.
If you really want a clear image of this happening, try finding a pattern and adding as much of them as possible. If it doesn't diverge, you'll see that it will start to approach a certain number. If it does, well, you'll just keep getting a bigger and bigger number until your calculator explodes.