Consider the recurrence equation defining T(n): T(n)=1 if n-1; T(n)=T(n-1)+2^n Otherwise . Show by induction T(n)=2^(n+1)-1

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Question

Consider the recurrence equation defining T(n): T(n)=1 if n-1; T(n)=T(n-1)+2^n Otherwise . Show by induction T(n)=2^(n+1)-1

Consider the recurrence equation defining T(n):

T(n)=1 if n-1;

T(n)=T(n-1)+2^n Otherwise .

Show by induction T(n)=2^(n+1)-1

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Answer 1

Answer #1

Given That, T (n)=1, if n=o. T(n) = T(n-1) + an other wise show by induction T (n) = 2 Proof by induction nt 2. Base Case - f step2 (- assume That it is true for Kel T (K) = 2 is true. now we have to prove it for n=k+1 for n=k+1 Step3 K+| K+/ L.H.S: T

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Answer 2

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Consider the recurrence equation defining T(n): T(n)=1 if n-1; T(n)=T(n-1)+2^n Otherwise . Show by induction T(n)=2^(n+1)-1