Write 1 r r2 r3 r4 r5 in sigma sigma notation Write k

Write 1 - r + r^2 - r^3 + r^4 - r^5 in sigma sigma notation. Write (k + 1)^3 + sigma_i = 1^k i^3 as a simple summation. Truns form sigma_k = 0^5 k (k - 1) by making the change of variable i = k + 1. Define the difference B - A, where A and B are each sets. Write the power set P ({x, y}) in set roster notation Let A = {4, 5, 6} and B = {7, 8}, write the set A Times B in set roster notation.

Solution

(30) ANS (-1)^n-1SIGMA n=1 to 6 r^n-1 (31)ANS SIGMA i=1 tok+1 i^{3 (32)ANS}SIGMA i=1 to6 (i-1)(i-2) (33)ANS B-A={x:xbelongs toB,x does not belong toA} (34) ANS { },{x}.{y},{x,y} (35) ANS { (4,7),(4,8),(5,7),(5,8),(6,7)(6,8)}