Home computickets Amount N of the first natural numbers and the sum of (n-1)

# Amount N of the first natural numbers and the sum of (n-1)

Author

Date

Category Hello, you can tell me where the formula of 2 lines is displayed. In 1 it is clear this is the sum of the first NAT. numbers, but why in 2 formula appears minus in brackets? Thank you.

Actually, that’s all – the text is needed only to drop 30 characters 🙂 however, here’s another explanation: everything is simple to paint and get

`Summ _ j = 2 ^ n (j-1) = 1 + 2 + 3 + 4 + 5 + ... + n-1 `and this is the arithmetic progression `n * ( N-1) / 2 `

and formula 1) and formula 2) can be proved with the help of mathematical induction

1. We will verify loyalty at `n = 2 `: `Sum = J - 1 = 2 - 1 = 1 = 2 (2-1) / 2 = 1 `– True

2. Let the formula are true for n, check it with `k = n + 1 `, we get

``````n (n - 1) / 2 + n = (k-1) (k-2) / 2 + (k - 1) = (k ^ 2 -3k + 2 = 2k - 2) / 2 = k (k-1) / 2 - right
``````

Formula proved

Why spend time searching for the correct question and then entering your answer when you can find it in a second? That's what CompuTicket is all about! Here you'll find thousands of questions and answers from hundreds of computer languages.