1. a) Compute the following sums (10 points): S₁ = 1+3+5+7+...+1999 S₂ =1+2+4+8+16+....+2048 n-1 n-1 n-1 =Σ³i S₁ =3i S₁ =Σ(2-1) S₁ = 3+1 i=1 i=0 i=0 b) Find the order of growth of the following sums. Use the ②(g(n)) notation with the simplest function g(n) possible (8 points): n-1 i=0 n-1 n n-2 n-1 n+1 ΣΣ2:1 (i+n) logi" 2"* Σ i=2 c) Prove the formula (3 points): n Zin(n+1)/2 i=1 i=1 i=0 j=i either by mathematical induction or by following the insight of a 10- year-old school boy named Carl Friedrich Gauss (1777-1855) who grew up to become one of the greatest mathematicians of all times.