Find the sum of the following numbers without actually adding them1+3+5+7+9+11+13+15

S = 1 + 3 + 5 + ... + 11 + 13 + 15

S = 15 + 13 + 11 + ... + 5 + 3 + 1

==>  2S = (1 + 15) + (3 + 13) + (5 + 11) + ... + (15 + 1)

There are 8 terms in the sum, so

2S = 8 * 16 = 128

S = 128/2 = 64

5

step-by-step explanation:

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints