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The number of tournament games is represented as...

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The number of tournament games is represented as...

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The number of tournament games is represented as G(n) where n is the number of attendees of the games. 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the attendees number is 30, what is the total number of games?

A. 380
B. 435
C. 455
D. 510
E. 520

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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LUANDATO wrote:
The number of tournament games is represented as G(n) where n is the number of attendees of the games. 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the attendees number is 30, what is the total number of games?

A. 380
B. 435
C. 455
D. 510
E. 520

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
G(n+1)=G(n)+n

G(2)=1
G(3)=G(2)+2 = 1+2 = 3
G(4)=G(3)+3 = 1+2 + 3
G(5)=G(4)+4 = 1+2 + 3+4

i.e. G(30)=1+2 + 3+4+5+.......+29 = (1/2)*29*(29+1) = 29*15 = 435

Answer: option B

I hope this helps!

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Hello LUANDATO.

In this question we will use the Gauss Sum, which says that the sum of the integers from 1 to n is $$\frac{n\cdot\left(n+1\right)}{2}.$$
It tell us $$G\left(n+1\right)=G\left(n\right)+n, and \ G\left(2\right)=1.$$
So, $$G\left(3\right)=G\left(2\right)+2=1+2.$$ $$G\left(4\right)=G\left(3\right)+3=1+2+3.$$ $$G\left(5\right)=G\left(4\right)+4=1+2+3\ +5.$$ As you can see, we can say that $$G\left(n\right)=1+2+3 +.\ .\ .\ +\ \left(n-1\right).$$ In other words, G(n) is the Gauss Sum from 1 to n-1.
So, $$G\left(30\right)=1+2+3 +\ .\ .\ .\ +\ 29\ =\ \frac{29\cdot30}{2}=15\cdot29=435.$$
The correct answer is B .
I hope this explanation may help you.
I'm available if you'd like a follow up.

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