Im having some trouble solving this Homework.

5. For $1; = 1']; :k_11 Verify that Z a... = Length of the interval [5, a] k=1 6-. Write out each summation and simplify the result. {a} i [.2 tic12F] k=l {b} i [.3 {k 12F] k=l Sum Formulas: ik= n{:n.+l} k=1 2 if? = n.{n+ 1}{2n+1] .=. :3. 25:3 = (RIDES1}): T. Use the sum formulas ahmre to evaluate each sum. [a]. E [3+2k+k2} k=l {In} 5 WM 1} k=1 {:1 i We 31 k=l 1. Compute the area under the function f(2) = 1-r and above the r - aris from : = 0 to r = 1. 2. Write each sum in sigma notation (a) 3+4+5+ ...+93 +94 (b) 4+6+8+...+24 (c) 9 + 16 + 25 + 36 + ... + 144 (d) its t ist ... + 100 (e) 3 +6+9+ ...+30 3. For this problem use the following table k bk 2 2 2 1 2 3 3 2 to verify the equality (30k - 2bk) = 3 ak - 2 I box 4. Let f(x) = r' and g(x) = 3r. Evaluate each sum: (a) E f ( k) K=O (b) E g(m) m=1 (c) E g(f(k)) K=1