Please proof by the substitution method, and recursive tree prove the upper bounds only. Thumbs up...

Question

Question

Please proof by the substitution method, and recur

Answer 1

Answer #1

1)

T(n) = T(n-1) + 1/n = T(n-2) + 1/n-1 + 1/n
= T(n-3) + 1/n-2 + 1/n-1 + 1/n
= T(n-4) + 1/n-3 + 1/n-2 + 1/n-1 + 1/n

==> T(n)=T(0) + Sigma pow n base i=1 1/i = 1+H base n

where HnHn are the harmonic numbers.

Answer 2

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