Summing series: Method of differences. Watch

chatterclaw73
Badges: 9
Rep:
?
#1
Report Thread starter 2 months ago
#1
Put 1/(r-2)r into partial fractions and use your result to show that the sum from r=3 to n is 3/2 - 1/(n-1) - 1/n.
I have set r to various values and using the method of differences, I have obtained
3/4 - 1/2n -1/2(n-1) which is twice the answer. What have I done wrong? Thanks for any advice in advance.
0
reply
RDKGames
Badges: 20
Rep:
?
#2
Report 2 months ago
#2
(Original post by chatterclaw73)
Put 1/(r-2)r into partial fractions and use your result to show that the sum from r=3 to n is 3/2 - 1/(n-1) - 1/n.
I have set r to various values and using the method of differences, I have obtained
3/4 - 1/2n -1/2(n-1) which is twice the answer. What have I done wrong? Thanks for any advice in advance.
Post your working out ?
0
reply
chatterclaw73
Badges: 9
Rep:
?
#3
Report Thread starter 2 months ago
#3
(Original post by RDKGames)
Post your working out ?
1/(r-2)r = 1/2(r-2) - 1/2r
Summation:

r=3: 1/2(1) - 1/2(3)
r=4: 1/2(2) - 1/2(4)
r=5: 1/2(3) - 1/2(5)
r=6: 1/2(4) - 1/2(6)
. . .
. . .
. . .
r=(n-3): 1/2(n-5) - 1/2(n-3)
r=(n-2): 1/2(n-4) - 1/2(n-2)
r=(n-1): 1/2(n-3) - 1/2(n-1)
r=(n) :1/2(n-2) - 1/2n

All terms cancel except
1/2(1), 1/2(2), -1/2(n-1), -1/2n, which when added, give
3/4 - 1/2(n-1) - 1/2n.
0
reply
ghostwalker
  • Study Helper
Badges: 17
#4
Report 2 months ago
#4
(Original post by chatterclaw73)
Put 1/(r-2)r into partial fractions and use your result to show that the sum from r=3 to n is 3/2 - 1/(n-1) - 1/n.
I have set r to various values and using the method of differences, I have obtained
3/4 - 1/2n -1/2(n-1) which is twice the answer. What have I done wrong? Thanks for any advice in advance.
If you set n=3 as a check, you can see that 1/(r-2)r = 1/3.

Their formula gives 2/3

Yours gives 1/3

Ergo, you right, them wrong.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Hertfordshire
    All Subjects Undergraduate
    Sat, 22 Feb '20
  • Ravensbourne University London
    Undergraduate Open Day Undergraduate
    Sat, 22 Feb '20
  • Sheffield Hallam University
    Get into Teaching in South Yorkshire Undergraduate
    Wed, 26 Feb '20

People at uni: do initiations (like heavy drinking) put you off joining sports societies?

Yes (370)
67.27%
No (180)
32.73%

Watched Threads

View All