Find the value of x=20132013xxxsgn(x)\sum\limits_{x=-2013}^{2013} x \cdot |x| \cdot \lfloor x \rfloor \cdot \text {sgn} (x) .

Here, x\lfloor x \rfloor denotes the greatest integer function or floor function, and sgn(x)\text {sgn} (x) denotes the sign function: 1 if xx is positive, 0 if xx is zero, and -1 if xx is negative.

I have invented this question, and got the answer 0\boxed{0} (correct me if I'm wrong), but I don't know how to solve this without using graphs. Please help. Thanks.

Note by Jaydee Lucero
6 years, 10 months ago

No vote yet
3 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

Note that x=x\lfloor x \rfloor = x as xx is an integer, and xsgn(x)=x|x| \cdot \text{sgn}(x) = x for all xx. So you're basically asking x=20132013x3\displaystyle\sum_{x=-2013}^{2013} x^3, which is now easy to solve.

Ivan Koswara - 6 years, 10 months ago

Log in to reply

Precise! So 0 is correct answer.

Piyushkumar Palan - 6 years, 10 months ago

Log in to reply

To evaluate the sum, note that terms of opposite signs cancel, and the only term left is 03=0.0^3 = 0.

Michael Tang - 6 years, 10 months ago

Log in to reply

now I see... thanks... :D

Jaydee Lucero - 6 years, 10 months ago

Log in to reply

by graph: The above function takes values of x on the X-axis and y=f(x) on the Y axis. this question is basically to plot the graph of f(x)=x^3, here we are only taking the integers values at x-axis and getting correspond y values as integers.So instead of smooth curve we will will be having the points which lies on the curve of f(x)=x^3.

Shubham Namdeo - 6 years, 10 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...