844 views

2 Answers

Best answer
6 votes
6 votes

Let $X=\frac{n(5n+1)(10n+1)}{6}$

For $n=1,  X= \frac{6*11}{6}=11$

For $n=2,  X=\frac{2*11*21}{6}=77$

For $n=3,  X=\frac{3*16*31}{6}=248$

For $n=4,  X=\frac{4*21*41}{6}=574$

Here, we can see $X$ is not divisible by $3$ and $5$ but $X$ is always an Integer.

Hence, Option(C) Is always an integer.

selected by
3 votes
3 votes

Option A and B can be eliminated easily, if you take n = 2 you get value of the given expression 

let X=n(5n+1)(10n+1)/6

=2(5*2+1)(10*2+1)/6

=77   --- which is neither divisible by 5 nor divisible by 3, Hence option A and B eliminated.

Option C

Proof by Induction:

Hence option C is correct.

edited by
Answer:

Related questions

2 votes
2 votes
2 answers
1
go_editor asked May 19, 2016
786 views
The area of the largest square that can be drawn inside a circle with unit radius is$\sqrt{2}$$2$$1$None of the above