Use the Summatioi formulasS to Ite the expressioi witriouL the surimation nolationI. 6k(k – 1) n3 k= 1 S(n) = Use the result to find the sums for n = 10, 100, 1000, and 10,000. n- 10 n = 100 n = 1,000 n = 10,000

Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for COS (+). with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.) f(x) = 1 + cos a -π SX ≤ π, b

a. Use the sum formulas to find the numerical value. 50 (4k2 + 3)   k = 1 b. Use the sum formulas to express the following without the summation symbol.   n   1 −  i2 n2     3 n     i = 1

Cs101, and 30 have taken CS102. 18 students have taken both. How many students are there 2. Suppose that every student in class has taken either CS101 or CS102. 45 students have taken Hìnt: You can use the formula: 12 = n(n + 1)(2n + 1)/6 in one of the questions. 1. Compute the value of each of these sums. Show the process of computation. 80 40 30 ( a) Σ (b) Συ/2 + 5) (b) i/2+ 5) (c) (2' +4) i=40 i=1 i=1 Hint: You can use the formula: i2 n(n + 1)(2n + 1)/6 in one of the questions. %3D %3D1 in class?