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1. When n=1, equation ① is calculated as,

Left Hand Side = 1

Right Hand Side = 1

2. Assuming that n=k is valid,

1 + 3 + 5 + … + (2k-1)=k ②

When n=k+1, the left hand side of ① is written as

1 + 3 + 5 + … + (2k-1)+(2k+1)

=k + (2k+1) (Obtained from equation ①)

=(k+1)

In other words,

1 + 3 + 5 + … + (2k-1)+(2k+1)

=(k+1)

① is valid when n=k+1.

From 1. and 2., equation ① is valid for all ...

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Power Ranking

Note

The numbers refer to existential value, and all lifeforms has it.

ADVENTURER GUILD POWER RANKING

Lv 1 - 20 = F (1 - 49)

Lv 20 - 30 = E (50 - 99)

Lv 30 - 50 = D (100 - 499)

Lv 50 - 60 = C (500 - 999)

Lv 60 - 80 = B (1,000 - 4,999)

Lv 80 - 100 = A (5,000 - 9,999)

Lv 100 - 200 = S (10,000 - 19,999)

Lv 200 - 500 = SS (20,000 - 29,999)

LV 500 - 900 = SSS (30,000 - 49,999)

LV 900 - 1000 = XS (50,000 - 99,999)

SPIRITUAL ENTITY RANKING SYSTEM BELOW

■MONSTERS AND OTHER NON-HUMAN LIFEFORMS

●Apocalypse > 100,000,000 - 1,000,000,000

●Armageddon > 10,000,000 - 99,999,999

●Cataclysm > 1,000,000 - 9,999,999

●Disaster > 100,000 - 999,999

■HUMAN

●Transcendent > 100,000,000 - 1,000,000,000

●Warlord > 10,000,000 - 99,999,999

●Mystical > 1,000,000 - 9,999,999

●Heroic > 100,000 - 999,999