I am having difficulty dealing with this question if you could provide the steps I would highly appreciate it.

You may use the sheet of Useful Math Relations provided on the course web site. 1-1 s = E 1. (27 points) a) Compute the following sums (10 points): S, =1+3+5+7+ ..... +79 S, =1+2+4+8+16+ ... +1024 C7i S. =(211) S =24*** b) Find the order of growth of the following sums. Use the g(n)) notation with the simplest function g(n) possible (12 points): 1-2 -1 logi" ZX 5(ij) i=0 j=i c) Prove the formula (5 points): i = n(n+1)/2 i=1 either by mathematical induction or by following the insight of a 10- year-old school boy named Carl Friedrich Gauss (17771855) who grew up to become one of the greatest mathematicians of all times. i2"+1 i=0