>> (p.1)
    Author Topic: Number of Merits generated (mathematically)  (Read 529 times)
    r1s2g3 (OP)
    Sr. Member
    ****
    Offline Offline

    Activity: 742
    Merit: 395


    I am alive but in hibernation.


    View Profile
    September 20, 2018, 04:50:52 AM
    Merited by Welsh (2), TMAN (2), DdmrDdmr (1), paxmao (1), The Cryptovator (1), stingers (1), Piggy (1), vlad230 (1), HiDevin (1)
     #1

      
    Quote
    There are 120 merit sources with a total merit generation of up to 23045 sMerit per 30 days

    When 1 Merit is given it generate .5 sMerits. I found many times user trying to calculate like from 23045 will create 11522 and then 5761  and so on.
    But they are not able to reach the number at end (after all the sum of halving merits).

    So I decided to calculate it Mathematically. Since number of smerits will halved every time and 23045 is not perfectly divisible by 2.
    We need to represent 23045 as sum of numbers that can be easily divisible by 2 at every stage till we reach Merit 1 .

    In other words, first we need to put 23045 as sum of numbers in power of 2

    23045 = 16384+4096+2048+512+4+1
    23045= 214 + 212 + 211 + 29 +22 +20

    Now we start with  214 i.e  16384 and check how many merits it can generate.

    16384 + 8192   + 4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1 =  32767
      
    Similarly, for other terms
    4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1 =                              8191
    2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1 =                                          4095
    512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1 =                                                                1023
    4 + 2 + 1 =                                                                                                                                7
    1=                                                                                                                                              1

    So sum of these number will be  32767+8191+4095+1023+7+1=46084
    Since we have 6 number that make up to the sum of 23045 , so  we get 6/2 =3. and further 3/2 =1
    You might be wondering why I did not use same formula for 6 (22+21 ) because 6 is converted to merit ,it is not smerit anymore.

    So in total 46084+3+1 = 46088 Merit will be generated Mathematically.

    This all calculation is derived by using the fundamentals of Geometric Progression and sequence, their nth term and sum till the nth term.

    Some links to understand Geometric Progression are here  and  here and here

    Tabular Data of the Calculation



    Hope you all enjoyed the calculation.

    PS: 46088  is mathematically feasible and maximum limit that can be generated if we used all source merit but actual number can be less or more because many users will left with residual smerits but this residual smerit can be used next time when they receive a single merit or odd number of merits.




    I am alive
Page 1
Viewing Page: 1