Re: [PrimeNumbers] solve using induction to find the sequence
- In a message dated 29/04/03 22:51:04 GMT Daylight Time, luken2u@...
> i have a problem that i can't figure out.. and i need to know how toAssume that, for 0 <= k < n
> do this b4 10 tonight... here is the problem (using induction)
> prove by induction
> let e (sub 0) = 1,
> e (sub 1) = 4
> and for n >1.
> let e sub n = 4[e (sub n - 1) - e (sub n-2)]
> what are the first six terms of the sequence?
> prove that e(sub n) = 2^n(n+1)
e_k = (k+1)*2^k (1)
e_n = 4*[e_(n-1) - e(n-2)]
= 4*[n*2^(n-1) - (n-1)*2^(n-2)]
= 2*n*2^n - (n-1)*2^n
So if (1) is true for k < n, it is true also for k = n.
But (1) is true for n = 0 and n = 1.
So (1) is true for all n >= 0.
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