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
Your topic reminds me of the old days in high school. Smerits are generated like radioactive decay and above sum is a geometric progression
I still remember that there's a general method to calculate this sum:
Assume that S = 16384 + 8192 + 4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1
= 2
14 + 2
13 + 2
12 + ... + 2
1 +2
0 (*)
then 2S = 2
15 + 2
14 + 2
13 + ... +2
2 +2
1 (**)
(**) - (*) side by side, then S = 2
15-1 = 32767
Btw, it's an interesting discovery OP.
I know, I can directly use the formula, but I just wanted it to be in laymen terms, where everybody can visualize each divison and the sum.
I like the analogy of sMerits vs radioactive decay but only difference is that they do not produce any unwanted product (like radiations)