What's a series
what is the difference between sequence and series
(What is) A sequence is a list of numbers. A series adds them together.
Is 1 + 2 + 3 + 4 + ... geometric?
Answer: (what is) no, the numbers don't multiply by the same ammount each time
What does it mean if a series converges?
(what is) it adds up to a real number, the sum approaches a limit
What does this series look like? 2 + 4 + 6 + 8 + ...
(What is) It’s an arithmetic series (adds 2 each time).
Is 1 + 2 + 4 + 8 + 16 geometric?
(what is) yes, each term multiplied by 2
What does it mean if a series diverges?
(what is) it keeps growing or doesn’t settle, no fixed sum
What does this series look like? 3 + 6 + 12 + 24 + ...
(What is) A geometric series (multiplies by 2 each time).
What is the common ratio in 81 + 27 + 9 + 3?
(what is) 1/3, each term is one third of the last one
Does the series 5 + 2.5 + 1.25 + ... converge or diverge?
(what is) converge, because the terms get smaller and add up
What’s the 5th term in this series? 5 + 10 + 20 + ...
(What is) 80
Is the series 5 + 15 + 45 + 135 geometric, and what is its common ratio?
(what is) yes, the common ratio is 3, each term triples
Does the series 1 + 2 + 4 + 8 + ... converge or diverge?
(what is) diverge, because the terms grow without limit
What do you call a series that never ends?
(What is)An infinite series
Is the series 500 + 150 + 45 + 13.5 geometric? If yes, what is the common ratio?
(what is) yes, the common ratio is 0.3, each term multiplied by 0.3 or 3/10
Does the series 500 + 500 + 500 + ... converge or diverge?
(what is) diverge, because terms don’t get smaller