1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Make a conjecture about the sum? Confused on what they want exactly

  1. Oct 2, 2006 #1
    Hello everyone,

    I'm confused on the directions. It says, Evalute the sum, for n = 1, 2, 3, 4, and 5. Make a conjecture about a formula for this sume for general n, and prove your conjecture by mathematical induction.

    This is the sum and my work:
    http://img351.imageshack.us/img351/9551/2pq2.jpg [Broken]

    I'm having a hard time figuring out that formula, and what exactly is a conjecture? In the other readings and this one they don't say anything about a conjecture.

    I was thinking that maybe they just want me to place an n where the k is?
    like n/(n+1)! ?

    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 2, 2006 #2


    User Avatar
    Homework Helper

    Why don't you actually add up the fractions? You should see a pattern emerge.
  4. Oct 2, 2006 #3
    I kind of see a pattern at the very last 2 terms,
    it goes from 119/120 to 719/720, the numerator is incremented by 600 and the denominator also by 600.
    But before that it goes
    n = 1
    n = 2
    n = 3
    n = 4
    n = 5
    n = 6

    if i keep going i get
    n = 7

    Oo i see it now hah...

    The denominator is +1 the numerator
    but if i use n that won't work for all cases.
    n/n+1, n >= 1

    Is there a technique to approach conjectures? I see the pattern but i don't see how n is producing the numbers.
  5. Oct 2, 2006 #4


    User Avatar
    Homework Helper

    The denominators are 1,2,6,24,120,... Do you recognize these?
  6. Oct 2, 2006 #5
    I know they are factorials, like
    1! = 1
    2! = 1*2 = 2
    3! = 1*2*3 = 6
    4! = 1*2*3*4 = 24
    5! = 1*2*3*4*5 = 120

    which is 1/n!
  7. Oct 2, 2006 #6
    I think i got it, am i allowed to write the following?

    Let n be an integer, where n >= 2 such that Sumnation k = 2 to n (n!-1)/n!

    THis also doesn't work i just saw, because i can't change the orginal sum, which is letting k = 1, i can't just change it can i?

    Is this what a conjecture is? I'm guessing the pattern of the output and I must prove the right and left are equal?

    http://img445.imageshack.us/img445/5030/lastscanrf1.jpg [Broken]
    Last edited by a moderator: May 2, 2017
  8. Oct 2, 2006 #7


    User Avatar
    Homework Helper

    Well then just use (n+1)! instead of n!. By "conjecture" they mean find a formula that seems right (works for low numbers). Then you need to prove the formula is correct using induction.
  9. Oct 2, 2006 #8
    Ahh yes! it works, thanks a ton Status! :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook