integral part of x = an integer n such that n

Question

= integral part of x = an integer n such that n <= x < (n+1)

Find   +   +   +   + ... +  .

AkamaiBrah · Answer

(2^1001-2)/3 - 500

Can you confirm?

Zhung Gazi · Answer

I dont have the answer, but the following is what I've got

  = (-1/2)+(1/6)*(-1)^n +(1/3)*2^n

Answer = (-1001/2)+(1/6)+(1/3)(2^1001-1)

kpadma · Answer

I got (2^1001) / 3. 

Could you explain why you are subtracting 500.

Zhung Gazi · Answer

BTW, the answer should be an integer. But 2^1001/3 is not.

AkamaiBrah · Answer

If you look at your answer closely, you will see that it is the same as mine.

AkamaiBrah · Answer

Simplest way to solve this is to assume geometry series of 1001 terms. 

If you examine terms, you will notice that rounding every odd and even term subtracts 1/3 and 2/3 respectively. Hence, the answer is the sum of the series or 1/3*(2^1001-1) less the sum of the rounding 500(1/3+2/3) + 1/3 which simplifies to the answer I gave.

kpadma · Answer

My Bad, I didn't read the question stem properly
I've interpreted   as just ().

  = integral part of x = an integer n such that n <= x < (n+1) 
is the key !

Thanks Akamai

integral part of x = an integer n such that n <= x <

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards