Question

the value after subtracting the sum of first natural numbers from sum of their first (n-1) natural numbers
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Answer 1

Answer:

n

Step-by-step explanation:

sum of first n-1 natural numbers

= n(n-1)/2 --A

sum of n natural numbers

=n(n+1)/2 --B

B-A

=( n/2)(n+1-n+1)=n

Answer 2

The value after subtracting the sum of first n natural numbers from the sum of their first (n - 1) natural numbers is (- n).

Correct question:

The value after subtracting the sum of first n natural numbers from the sum of their first (n - 1) natural numbers

Concept to be used:

Before we solve this problem, we must know that the sum of the first n natural numbers is

$\dfrac{n(n+1)}{2}$

Step-by-step explanation:

The sum of the first n natural numbers

= $\dfrac{n(n+1)}{2}$

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

= $\dfrac{(n-1)(n-1+1)}{2}$

= $\dfrac{n(n-1)}{2}$

Thus the required subtraction

= the sum of first (n - 1) natural numbers - the sum of first n natural numbers

= $\dfrac{n(n-1)}{2}-\dfrac{n(n+1)}{2}$

= $\dfrac{n}{2}(n-1-n-1)$

= $\dfrac{n}{2}(-2)$

= - n

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