9/8/2015 Algebra Problem on Telescoping Series ­ Sum: Find the floor ­ Sanjeet Raria | Brilliant

https://brilliant.org/problems/my­observations­in­math­1/ 1/5

1 solutionVote up solutions you admire

Correct answer: 7

Krutarth Patel

22, India

Solution writing guide: Level 5

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Ayush Verma

19, India Upvote (29) Nov 22, 2014

this is telescoping,

Now use calculator,

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Sanjeet Raria

21, IndiaNov 23, 2014

Another way of approaching this question could be to know that

Now the series can easily be telescoped to get the result.

@Pranjal Jain @Ayush Verma @sandeep Rathod

7 0 Reply

Calvin Lin STAFF

30, USANov 24, 2014

In response to Sanjeet Raria: I like Ayush's method, as it easily generalizes andshows us how to deal with for some polynomial . It doesn't

involve trying to spot a "magical" equation, but shows us how we can derive it.

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9/8/2015 Algebra Problem on Telescoping Series ­ Sum: Find the floor ­ Sanjeet Raria | Brilliant

https://brilliant.org/problems/my­observations­in­math­1/ 2/5

← Find the floor · Level 5 (220 points)

If the general term of a series is

and if

then find

This is one of my original problems.

Next problem

involve trying to spot a "magical" equation, but shows us how we can derive it.

2 0 Reply

Sanjeet Raria

21, IndiaNov 24, 2014

In response to Calvin Lin: Ayush's method is brilliant no doubt in that but theequation I've written down is not magical since everyone can reach it in a moregeneralized and simple way. I am going to explain this in my upcoming note.

(last modified 9 months ago )

2 0 Reply

Calvin Lin STAFF

30, USANov 25, 2014

In response to Sanjeet Raria: I look forward to learning about that! It will helpsuch telescoping sums to be able to quickly figure out how to get

.

2 0 Reply

Sanjeet Raria

21, IndiaNov 25, 2014

In response to Calvin Lin: Exactly sir.

1 0 Reply

Pranjal Jain

17, IndiaNov 22, 2014

How can someone think of telescoping here?? Awesome!!

2 0 Reply

Calvin Lin STAFF

30, USANov 24, 2014

In response to Pranjal Jain: That is quite natural in the context of this question.You may be familiar with the case of . This is often

done with induction, but the better approach is to use telescoping series andrecognize it as .

Hence, we want to do something similar. The easiest way to generalize it to tolook at . This gives a way to

motivate the rest of the proof.

(last modified 9 months ago )

3 0 Reply

Pranjal Jain

17, IndiaNov 24, 2014

In response to Calvin Lin: Nicely explained! Thanks! You too @Ayush Verma

(last modified 9 months ago )

1 0 Reply

Shashank Rustagi

20, IndiaJun 18

9/8/2015 Algebra Problem on Telescoping Series ­ Sum: Find the floor ­ Sanjeet Raria | Brilliant

https://brilliant.org/problems/my­observations­in­math­1/ 3/5

Actually It is 7.9018827

1 0 Reply

Megh Choksi

18, IndiaNov 29, 2014

Hats off . Upvoted

This image is copied from John Muradeli comment

1 0 Reply

Sandeep Rathod

28, IndiaNov 22, 2014

Sir how did you factorized it? @Ayush Verma

(last modified 9 months ago )

1 0 Reply

Ayush Verma

19, IndiaNov 22, 2014

In response to Sandeep Rathod: Method 1

Method 2

(last modified 9 months ago )

6 0 Reply

9/8/2015 Algebra Problem on Telescoping Series ­ Sum: Find the floor ­ Sanjeet Raria | Brilliant

https://brilliant.org/problems/my­observations­in­math­1/ 4/5

Sandeep Rathod

28, IndiaNov 23, 2014

In response to Ayush Verma: Really nice greatly done

1 0 Reply

Sanjeet Raria

21, IndiaNov 22, 2014

I appreciate your talent. Outstanding.

1 0 Reply

9/8/2015 Algebra Problem on Telescoping Series ­ Sum: Find the floor ­ Sanjeet Raria | Brilliant

https://brilliant.org/problems/my­observations­in­math­1/ 5/5

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