SIGMA NOTATION The capital letter sigma, , is used to indicate summation. 8 x means find the sum of the x terms for every consecutive integer x, from x = 4 x 4 through x = 8. The x in this notation represents the index. The lower limit or starting value of the index appears below the sigma while the upper limit or ending value of the summation is above the sigma. EXERCISES: 3 1. What is the value of (2m 1) m1 ? m 1 5 2. What is the value of (m 2 1) ? m 2 3. If nCr represents the number of combinations of n items taken r at a time, what is the 3 value of 4 Cr ? r 1 3 4. What is the value of (2 (b)i ) ? b0 5 5. Evaluate: 2 (2n 1) n 1 7 6. Evaluate: (3i 2) i 4 10 7. Find the value of ( j 6) 2 . j 7 4 8. Evaluate: tan(n ) n0 4 9. Find the value of 5 Cr . r 2 10. A ball is dropped from a height of 8 feet and allowed to bounce. Each time the ball bounces, it bounces back to half its previous height. The vertical distance the ball F1 I travels, d, is given by the formula d = 8 16 GJ, where n is the number of H2 K n k k 1 bounces. Based on this formula, what is the total vertical distance that the ball has traveled after 4 bounces? 11. The projected total annual profits, in dollars, for the Nutyme Clothing Company 2 from 2002 to 2004 can be approximated by the model (13,567n 294) , where n n0 is the year and n=0 represents 2002. Use this model to find the company’s projected total annual profits, in dollars, for the period 2002 to 2004.