Discrete math question Use mathematical induction to prove t

Discrete math question. Use mathematical induction to prove the above.

Summation j = 1 n j 2^j = (n - 1)2^n + 1 + 2

Let us prove for n=1

put n=1

LHS, 1.2=2

RHS = (1-1)2²+2 = 2

LHS=RHS

Hence P(n) is true.

Let us assume that P(k) is true.

P(k): (k-1)2^k+2+2

Now we have to prove that P(k+1) is true

P(k+1): (k-1+1)2^k+1+2+2

(k-1)2^k+1+2+2+2^k+1+2

2((k-1)2^k+2+2^k+2)+2

hence it is proved for P(k+1) also.

$Discrete math question. Use mathematical induction to prove the above. Summation j = 1 n j 2^j = (n - 1)2^n + 1 + 2SolutionLet us prove for n=1 put n=1 LHS, 1.2$

Discrete math question Use mathematical induction to prove t

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