Question

If the sum of the first ten natural numbers is $S_1$ and that of the first ten whole numbers is $S_2,$ then $S_1-S_2$ is 10.

• A. True
• B. False

Answer 1

The correct option is A

True

Sum of the first ten natural numbers:
The first ten natural numbers are 1, 2, 3, ..., 10.
$\Rightarrow a=1$ and $d=1$
$S_1=\frac{n}{2}(2a+(n-1\left)d\right)=\frac{10}{2}(2+9)=55$

Sum of the first ten whole numbers:
The first ten whole numbers are 0, 1, 2,..., 9.
$\Rightarrow a=0$ and $d=1$
$S_2=\frac{n}{2}(2a+(n-1\left)d\right)$
$=\frac{10}{2}\left(\right(2\times 0)+9)=45$

$\therefore S_1-S_2=55-45=10$