Question

If the sum of first n natural numbers is 1/5 times the sum of their squares then the value of n is

Answer 1

Please see the attachment

Answer 2

Answer:

The value of n is 7

Step-by-step explanation:

We know that,

Sum of first n natural  numbers = $\frac{n(n+1)}{2}$,

Also, the sum of square n natural numbers = $\frac{n(n+1)(2n+1)}{6}$

According to the question,

$\frac{n(n+1)}{2}=\frac{1}{5}\times \frac{n(n+1)(2n+1)}{6}$

$1 =\frac{1}{5}\times \frac{2n+1}{3}$

$15 = 2n + 1$

$14 = 2n$

$\implies n =\frac{14}{2}=7$

Learn more :

Show that sum of first n even natural numbers is equal to (n+1/n)times the sum of first n odd natural numbers

https://brainly.in/question/9817417