Find a formula for when m is a positive integer.

Chapter 1, Problem 41E

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QUESTION:

Find a formula for \(\sum_{k=0}^{m}\lfloor\sqrt{k}\rfloor\), when \(m\) is a positive integer.

Equation Transcription:

Text Transcription:

sum_k=0^m l floor k r floor

Questions & Answers

QUESTION:

Find a formula for \(\sum_{k=0}^{m}\lfloor\sqrt{k}\rfloor\), when \(m\) is a positive integer.

Equation Transcription:

Text Transcription:

sum_k=0^m l floor k r floor

ANSWER:

Solution:

Step 1:

 In this problem we need to find the formula for

                                     ,where m is a positive integer.

NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.

                     

                       

                       

                       

Example :  

                 

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