#Idk how to solve this

34 messages · Page 1 of 1 (latest)

tacit mural
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How do you solve this and what’s the answer lol

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heavy garnetBOT
turbid jacinth
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∞
∑ (48n + 172n)
n = 1

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@tacit mural Is this what you’re trying to say?

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It becomes
∞
∑ 220n
n = 1
If that’s so.

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But first I need you to confirm

tacit mural
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Yes

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@turbid jacinth

tacit mural
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So what would be the final answer?

turbid jacinth
turbid jacinth
tacit mural
turbid jacinth
# tacit mural Yeah a little bit

∞
∑ 220n
n = 1

This notation is describing a sum, specifically you are summing 220n from n = 1 all the way to n = ∞, but something cannot “equal” infinite, but it can approach it, so we say n → ∞, basically what this is saying is:
220(1) + 220(2) + 220(3) + 220(4) + 220(5) + 220(6) + 220(7) + 220(8) + 220(9) + 220(10) + … + 220n, where n → ∞

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Do you know what “divergence” and “convergence” means?

tacit mural
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Thank you for your help

turbid jacinth
# tacit mural I do not lol

Ok convergence means that the sum of the terms converge (approach) a finite value such as 1, 6, -2, π, e, 2/7, basically any number.

Divergence means the sum of terms does not approach a finite value, and the sum either indefinitely oscillates or simply grows without bound (∞)

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So if the sum converges , then there is a numerical answer, but if the sum does not converge then there isn’t really a numerical answer but we can say it is a divergent series, which lets us know the sum of the terms approach infinity, or don’t settle on one value — indefinitely oscillate (a series is the sum of a sequence of terms)

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@tacit mural just based on intuition, do you think the sum converges or diverges?

tacit mural
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Diverges…?

turbid jacinth
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Yes that’s right

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It’s a divergent series

tacit mural
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W teacher

turbid jacinth
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Because as you keep adding the terms up, it approaches infinity, an example is

220(1) + 220(2) + 220(3) + 220(4) + 220(5) + 220(6) + 220(7) + 220(8) + 220(9) + 220(10) = 12,100

For the first 10 n, the sum is already above 12,000, and as you keep adding to it indefinitely, it does not settle on a value and keeps increasing indefinitely

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So we say the sum equals infinity

tacit mural
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Ok that makes sense

turbid jacinth
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Do you know any calculus?
Because infinite series are primarily in the domain/study of calculus

tacit mural
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So the answer is n → ∞?

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No I don’t know any calculus I just saw this equation on the internet lol

turbid jacinth
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You would say

∞
∑ 220n = ∞
n = 1

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Or simply say “divergent”

turbid jacinth
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Well if you’re interested I can help you with another problem similar if you’d like

tacit mural
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Ok thank you for your help. You’re very informative