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Quote from: Wayshow on May 27, 2012, 04:23:34 am

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house of random = 0post count

you think i dont know that

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Lol WG Tom unit strong
Welcome!

This isn't technically right, but I know where it converges.
There is probably a way to "show" it converges, I'm just assuming it does.

Q11a)

a(n) = sqrt (3 + a(n-1))
a(n+1) = sqrt( 3 + sqrt (a(n))

a(n+1) = sqrt (3 + sqrt (3 + a(n-1)))

a(n+1) - a(n) = sqrt (3 + sqrt(3 + a(n-1))) - sqrt (3 + a(n-1))

If we assume series converges, a(n+1) - a(n) = 0

sqrt(3 + a(n-1)) = sqrt(3 + sqrt(3 + a(n-1)))

Square both sides

3 + a(n-1) = 3 + sqrt (3 + a(n-1)

a(n-1) = sqrt (3 + a(n-1))

Square again

a(n-1)^2 = 3 + a(n-1)

a(n-1)^2 - a(n-1) -3 = 0

a(n-1) = 2.302775637

Thats where your series converges.

What I've done is incorrect though, I find a(n-1) instead of a(n).
Unless we assume a(n-1) = a(n). But then I just assumed convergence instead of proving it.
I know it involves subtracting something like a(n+1) away from a(n) and showing it equals something.

On a side note, nobody uses this stuff in the real world anyway.

Ty for trying though

I can pretty much do everything on the calculus textbook....except sequences, series. The convergence question is just wtf lol

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Wats a mordor....
Have you ever listened to crappy opera?

I know of this woman.
She was super famous in her day.
People LOVED hearing her butcher shit.
I love her to bits lol.
And she's honestly trying her hardest!

Her confidence and earnest attitude is very inspiring. The accompanist is very good too, and never tries to lead her
Like the Rebecca Black of classical music