"Show that the sum of the first 2n natural numbers is n(2n+1)"

[aliasabc]

Could someone help I'm not sure how to do this.

"Show that the sum of the first 2n natural numbers is n(2n+1)"

gracias

[meboz]

try mathematical induction

[krtxmrtz]

There's an easy proof grouping the terms as follows:

Sum = 1 + 2 + 3 + ... + (n -1) + n + (n +1) + ... + (2n - 1) + 2n =

1 + 2n +
2 + (2n -1) +
3 + (2n -2) +
... +
n + (2n - (n - 1))

Now, you have a total of n sums of 2 terms, each of which is equal to 1 + 2n. Hence, Sum = n(1 + 2n)

QED

This is the method whereby Gauss outwitted all his school mates and his teacher.