This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Morning RÉSPÊÇT📿☝️.......🙏🙏🔐 — let's get this done. Here are the solutions for the given summations: a) We need to evaluate the sum _n=0^5 (2(n-3)). Step 1: Expand the term inside the summation. 2(n-3) = 2n - 6 Step 2: Write out each term for n from 0 to 5. For n=0: 2(0)-6 = -6 For n=1: 2(1)-6 = -4 For n=2: 2(2)-6 = -2 For n=3: 2(3)-6 = 0 For n=4: 2(4)-6 = 2 For n=5: 2(5)-6 = 4 Step 3: Sum all the terms. _n=0^5 (2n-6) = (-6) + (-4) + (-2) + 0 + 2 + 4 = -12 + 6 = -6 The sum is -6. b) We need to evaluate the sum _n=0^5 n(n+4). Step 1: Expand the term inside the summation. n(n+4) = n^2 + 4n Step 2: Write out each term for n from 0 to 5. For n=0: 0(0+4) = 0 For n=1: 1(1+4) = 5 For n=2: 2(2+4) = 12 For n=3: 3(3+4) = 21 For n=4: 4(4+4) = 32 For n=5: 5(5+4) = 45 Step 3: Sum all the terms. _n=0^5 (n^2+4n) = 0 + 5 + 12 + 21 + 32 + 45 = 115 The sum is 115. What's next?