Math Contest #24 Results and Solution



The problem of this contest was to find the limit of a converging sum:

This may look unsolvable at first, but it really isn't that hard. You can get to the result with just a bit of restructuring(Due to the lack of latex support at steemit I will use Σ to denote the sume from 1 to infinity. I also define L as the limit of the sum):
L = Σ 1/(x*(x+3)) = Σ (x+3 + 1 -x-3)/(x*(x+3))
= Σ (x+4)/(x*(x+3)) – Σ (x+3)/(x*(x+3))
= Σ (x+4)/(x*(x+3)) – Σ 1/x
Here it is possible to make an index shift by 3 on the right side(thus removing the first 3 terms from the sum and changing x). This is allowed because we know 1/xis converging to 0:
= Σ (x+4)/(x*(x+3)) – Σ 1/(x+3) – 1 – 1/2 – 1/3
= Σ (x+4)/(x*(x+3)) – Σ x/(x*(x+3)) – 1 – 1/2 – 1/3
= Σ (x+4 – x)/(x*(x+3)) – 3/2 – 1/3
= Σ 4/(x*(x+3)) – 11/6
= 4L – 11/6
↓ Rejoining the beginning and the end of this long set of equations
L = 4L - 11/6
3L = 11/6
L = 11/18


List of participants with their entries:

Namesolution foundcomment
@crokkonincorrect(0.611111100938577 with computer program)inaccurate and not done mathematical.


Winner draw:

Not necessary since only 1 successful participant:
Congratulations @tonimontana , you won 2 SBI!

The next contest starts soon. Don't miss it!


A bonus $trendotoken tip from ONECENT!
Also consider MAPR fund and MAXUV vote bonds too.
MAP Steem FinTech: growing your STEEM without SP.


Congratulations @quantumdeveloper! You have completed the following achievement on the Steem blockchain and have been rewarded with new badge(s) :

You published more than 80 posts. Your next target is to reach 90 posts.

You can view your badges on your Steem Board and compare to others on the Steem Ranking
If you no longer want to receive notifications, reply to this comment with the word STOP

To support your work, I also upvoted your post!

You can upvote this notification to help all Steem users. Learn how here!