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Given T(n)= T(n-1) + 2*n, using the substitution method prove that its big O for T(n)...

Given T(n)= T(n-1) + 2*n, using the substitution method prove that its big O for T(n) is O(n^2).

1. You must provide full proof.

2. Determine the value or the range of C.

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Answer #1

a)bb)

T(n) = T(n-1) + 2*n Than) ET (naz) + 2(n-1) sub 5 in O Tani: TCna 2) +2 (1-12 + 2n T(n-3) + 2(0-2) + 2(n-1) +2n = T (nak) + 2 fn-(k-1))+ . 2 n + To makes Nakal 2) Ken-1 - T() + 2 n-(n-1-1) + h - 17-1-2) + +1] e [n-o-1-1) [2+3+ T()) + 2 in] let T(1) = 1+2 [2+3+ .. un] Sum of natural nore T(n) n (+1) + Trên ) Tn) - 0 (m2)

(iting & Who gcna n 2 (W & ac g(n) utzu ch2- UtqU eht zu 2 utghe ; noi Ily 2 24 2 plo 9(n) ful (tu) u for c32 =olne)

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