NEED ASAP WILL RATE RIGHT AWAY 1,nEN s) (0 27.For thefollowing recurrence relation: T(1)2,T(n) 2(n1)z1,n a....

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NEED ASAP WILL RATE RIGHT AWAY
1,nEN s) (0 27.For thefollowing recurrence relation: T(1)2,T(n) 2(n1)z1,n a. Find the first 6 terms. b. Find the closed form solution.

1,nEN s) (0 27.For thefollowing recurrence relation: T(1)2,T(n) 2(n1)z1,n a. Find the first 6 terms. b. Find the closed form solution.

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Answer 1

Answer #1

The first six terms are:

T(1)= 2

T(2) = 2*T(1)-1= 3

T(3) = 2*T(2) - 1 = 5

T(4) = 2*T(3)-1 = 9

T(5) = 2*T(4)-1= 17

T(6) = 2*T(5)-1 = 33

So, the first six terms are 2,3,5,9,17,33.

b. Closed form solution:

T(n)= 2*T(n-1) - 1

= 2*(2*T(n-2)-1)-1

= 2*(2*(2*T(n-3)-1)-1)-1

= 2³T(n-3) -2²- 2 - 2⁰

= 2³T(n-3) - (2³-1)

= 2^n-1T(n-(n-1)) - (2^n-1-1)

= 2^n-1T(1) - (2^n-1-1)

= 2^n-1*2- 2^n-1 +1

= 2ⁿ- 2^n-1 +1?

So, closed form solution is T(n)= 2ⁿ- 2^n-1 +1?

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Answer 2

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