I was starting practice questions in this prep book and I do not understand how to solve 8) For each integer n> 1, let A(n) denote the sum of the integers from 1 to n. for example A(100)= 1+2+3…+100= 5,050. what is the value of A(200)? I have the answer, but I do not understand the text explanation or how to figure out this answer on my own, can anyone explain? thank you!
A(200) = A(100) + 101 + 102 + … + 200
A(200) = A(100) + (100 + 1) + (100 + 2) + … + (100 + 100)
A(200) = A(100) + 100 * 100 + (1 + 2 + 3 + … + 100)
A(200) = A(100) + 10000 + A(100)
A(200) = 2 A(100) + 10000
A(200) = 5050 * 2 + 10000
A(200) = 10100 + 10000
A(200) = 20100
Or just use the formula
Sum of first n integers is \frac{n(n + 1)}{2}. When n = 200, this gets us 1/2 (200 * 201) = 20100.