Summation!

Algebra Level 4

$\displaystyle \sum_{r=1}^{2013} ({1 + r^{-2} + (r+1)^{-2}})^{\frac{1}{2}} = \ ?$

Give your answer to 3 decimal places.

The answer is 2013.9995.

2 solutions

Nishant Rai
Apr 29, 2015

I think that question is from the magazine mtg PCMB today.

Shivam Jadhav - 6 years, 1 month ago

October 2013 edition. (15 Challenging Problems For Entrance Exams)

Nishant Rai - 6 years, 1 month ago

And here I was wondering why you chose 2013 instead of 2015 :P

A Former Brilliant Member - 6 years ago

@A Former Brilliant Member – good question, @Azhaghu Roopesh M .

i was practicing Sequence & Series, when my friend showed me this problem. I did it earlier in 2013 itself, but when i saw it again, i thought it's worth sharing $\ddot \smile$

Nishant Rai - 6 years ago

Nice solution. Before solving how can we think that that term will become zero and try this method

Shiwang Gupta - 6 years, 1 month ago

I got it right even though I entered 2013 , crazy right ?

Here's my Java code :

float s=0;
for(int r=1;r<=2013;r++)
{

    s= (float) (s + Math.pow(1 + (float) Math.pow(r,-2) + (float) Math.pow(r+1,-2), 1 / 2));

}

System.out.println(""+ s);

A Former Brilliant Member - 6 years ago

Jonathan Salim
May 3, 2015

Summation!

The answer is 2013.9995.

2 solutions

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