Question

For each of the summations given below, use the formula for the sum of the first n integers either to evaluate the sum or to express it in closed form. (a) 9 + 10 + 11 + 12 + ... + 700 (b) 9 + 10 + 11 + 12 + ... +k

Answer 1

The answers are

a) 245314

b) (k2 + k- 72)/2

a)

Let F(n) denotes the sum of first n natural numbers.

F(n) = (n(n+1))/2

9+10+11+12+13+----------------------+700

F(700) - F(8) = (700*701)/2 - (8*9)/2 = 490628/2 = 245314

b)

9+10+11+-------------------k

F(k) - F(8) = (k(k+1))/2 - (8*9)/2 = (k2 + k- 72)/2

Natural numbers are all positive numbers like 1, 2, 3, 4, and so on. They are the numbers you usually count and they continue till infinity.

Learn more about natural numbers here: brainly.com/question/24672369

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