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)?

Question

A.)10,100
B.)15,050
C.)15,150
D.)20,100
E.)21,500

I know that the best answer choice is D, but the explanation that I was provided doesn't help in understanding the concept. If someone could provide an explanation and the topic area that this type of mathematics that this would fall under to get a better understanding of the concept, I would greatly appreciate it.

Answer 1

A little research will turn up many proofs that A(n) = n(n+1)/2

One easy way is to divide the numbers into pairs, from both ends.

1,n
2,n-1
3,n-2
...
Each pair adds up to n+1
There are n/2 such pairs.
The result follows.

Answer 2

Thanks, so this falls under induction by reasoning, if I'm not mistaken?

Answer 3

proof by induction

Answer 4

Thanks