Math Is Fun Forum

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

finding formula for series

i have:

i've now worked out:

but im stuck on x[n], so far i have:

i think thats right... but if it is, im completely stumped on the last summation

Last edited by luca-deltodesco (2007-04-10 09:30:19)

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whatismath

Member

Registered: 2007-04-10

Posts: 19

Re: finding formula for series

I think from y_n to x_n, you make a mistake @ 2^(n-1) (2^n -1) which = (4^n - 2^n)/2.
But I think you have already make a mistake @ y_n:
y_n - 2^n(y_0) = (y_n -2y_(n-1)) + 2(y_(n-1)) - 2y_(n-2)) + ... +2^(n-1)(y_1 - 2y_0)
                       = 3z_(n-1) + ... + 3z_1 + 3z_0
                       = 3z_0(sum 4^k, k=0 to k=n-1)
                       = (4^n - 1)z_0

So y_n = 2^n(y_0) + (4^n - 1)z_0.

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: finding formula for series

Last edited by Stanley_Marsh (2007-04-10 11:14:54)

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Numbers are the essence of the Universe

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: finding formula for series

The same from y to x

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Numbers are the essence of the Universe