Anyone out there who can give me some tips and techniques on infinite series?

Such as taking the sum of a telescoping series ('cause I'm too lazy to write), and easily identifying divergence and convergence by looking at the equation.

I don't really need an answer, but I'd be very glad to learn some techniques. Thank you in advance.



I guess try to remember the strategies for testing series and of course answer sample problems in the book.

STRATEGY FOR TESTING SERIES (i summarized it...used stewart's calculus 7e as reference)

1) if it's 1/(n^P) -->> p-series. Convergent when p>1, divergent when p≤1

2)Σar^n -->> geometric series. Convergent when absolute value of r<1, divergent when  absolute value of r≤1

3) Test for Divergence

4) if it's multiplied my (-1)^n or something, it's probably an alternating series so use the alternating series test

5) factorials and other products? use the Ratio test

6) (b)^n Root test

7) Integral test

Look up Patrickjmt on youtube for more info. He has lots of calculus, algebra, trig,etc. tutorials

you can also try khanacademy
Hi figtreeacorn! I was losing hope for this question and I'm happy that someone answered. I looked up the sites you said and I bet I'd learn a lot from these. Thanks a lot!
you're welcome. It's cool you guys are taking calc1 in high school:)
I'm actually in college, there's just no option for college on the profile so yeah. :))
that explains it:) same here