2.25 (Review of summation notation) Let x1,

c, xn denote a sequence of numbers, y1,

c, yn denote another sequence of numbers, and

a, b, and c denote three constants. Show that

a. a n

i = 1 axi = aa n

i = 1 xi

b. a n

i = 1

(xi + yi) = a n

i = 1 xi + a n

i = 1 yi

c. a n

i = 1 a = na

d. a n

i = 1

(a + bxi + cyi)2 = na2 + b2a n

i = 1 x2i+ c2a n

i = 1 y2i

+ 2aba n

i = 1 xi +

2aca n

i = 1 yi + 2bca n

i = 1 xiyi