TI-83 Calculus 2 Calculator question
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TI-83 Calculus 2 Calculator question

[From: ] [author: ] [Date: 11-11-14] [Hit: ]
i already have that.-Not really, not without a third-party program at least.To find the series (i.e. the sum of a sequence) when the bound are finite,......
Ive read through the manual and have found nothing on it, so I'm assuming these calculators cant do what I'm looking for. Does anyone know if there's a way to find whether or not an infinite series converges? or a Series that does have an end converges? A general example of the type of equation I'm trying to put in is like in the picture below.

http://tinypic.com/r/2jbt7q0/5

--The answer is 1/192.. i already have that.

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Not really, not without a third-party program at least.

To find the series (i.e. the sum of a sequence) when the bound are finite, you can use the [Stat] > Math > 5:sum( and [Stat] > Ops > 5:seq( commands together.

Example: to find the series of (1/4)^n from n = 1 to 5, you could type in:
sum(seq((1/4)^N,N,1,5))

Finding the series or convergence of an infinite series isn't really possible, short of trying to discern the function's end behavior from a graph or using a program (which may or may not be reliable), such as http://www.ticalc.org/archives/files/fil…

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This is a geometric series.

S = (1/4)^4 + (1/4)^5 + (1/4)^6 + ... + (1/4)^t
S * (1/4) = (1/4)^5 + (1/4)^6 + ... + (1/4)^t + (1/4)^(t + 1)

S - S * (1/4) = (1/4)^4 - (1/4)^(t + 1)

t goes to infinity

S * (1 - 1/4) = (1/4)^4 - (1/4)^(inf + 1)
S * (3/4) = (1/4)^4 - (1/4)^(inf)
S * (3/4) = 1/256 - 0
S = (4/3) * (1/256)
S = (1/3) * (1/64)
S = 1/192

A calculator is a tool, not a crutch. If you can't do something, why should your calculator do it?
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