A.8y+4=60 B.4y+8=60C.8÷y+4=60D.y+8+4=60
2 answers:
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This sequence has generating function
(if we include for a moment)
Recall that for , we have
Take the derivative to get
Take the derivative again:
Take the derivative one more time:
so we have
<h3>Answer: 31 games</h3>
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Explanation:
- 32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
- 16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
- 8/2 = 4 games happen in round 3.
- 4/2 = 2 games in round 4.
- 2/2 = 1 game as the final championship.
Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.
To get the total number of games played, we add up the quotients
16+8+4+2+1 = 31
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Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1
We can write that rule as
which is equivalent to