# The sum of all natural numbers

Question:

The sum of all natural numbers ' $n$ ' such that $1001$ is :

1. (1) 3203

2. (2) 3303

3. (3) 3221

4. (4) 3121

Correct Option: , 4

Solution:

$\because 91=13 \times 7$

Then, the required numbers are either divisible by 7 or 13 .

$\therefore$ Sum of such numbers $=$ Sum of no. divisible by $7+$

sum of the no. divisible by 13 - Sum of the numbers divisible by 91

$=(105+112+\ldots+196)+(104+117+\ldots+195)-182$

$=2107+1196-182$

$=3121$

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