Question

The sum of first n natural numbers was calculated as 1850

Answer 1

Sn = n(n+1)/2
Sn= 1850

1850*2 = n2 +n

N2+N - 3700 =0

After solving n=60

Answer 2

The sum of ‘first n natural numbers’ was calculated as 1850 is not true

Given:  

The sum of “first n natural numbers” was calculated as 1850.

Solution:  

The natural numbers are the positive numbers as under:

1, 2, 3, 4, 5 and so on.  

We know that the sum of above referred natural numbers (n) is 1850.

Sum of the Arithmetic progression $=\mathrm{S}_{\mathrm{n}}=\frac{n(n+1)}{2}$

Whereas n = number of terms

Thus, 1850 = n(n + 1)/2

$\begin{array}{l}{1850 \times 2=\mathrm{n}^{2}+\mathrm{n}} \\ {3700=\mathrm{n}^{2} \times \mathrm{n}} \\ {\mathrm{n}^{2}+\mathrm{n}=3700}\end{array}$

That means n (n + 1) = 3700

By trial and error method, let us find n.

$\begin{aligned} 50(50+1) &=50 \times 51=2550 \\ 60(60+1) &=60 \times 61=3660 \\ 61(61+1) &=61 \times 62=3782 \end{aligned}$

Hence, the statement that the sum of first n natural numbers was calculated as 1850 is not true.