Missing number

Posted November 22nd, 2010 by manishaavalia

A child wants to add a first few natural number and he came up with the sum of 575. Unfortunately he missed a number. What is the missing number?

Comments

On November 23rd, 2010 Structure says:

We know

$S_n=1+2+...+n=\frac{n(n+1)}{2}$

Your missing sum is

$M_{sum}=1+2+...+n-k\ge 1+2+...+n-n=1+2+...(n-1)=S_{n-1}=\frac{(n-1)n}{2}$

$S_{n-1}<575<S_n$

We have

$S_{33}=561<575<s_{34}=595$

we have

$1+2+...+34-20=595-20=575$

On November 22nd, 2010 menestrel says:

Although i am pretty curious about the solving method.