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algebra intermediate

Problem

Given the set of

n

numbers;

n > 1

, of which one is

1 - \frac{1}{n}

and all the others are

1

. The arithmetic mean of the

n

numbers is:

(A)

1

(B)

n - \frac{1}{n}

(C)

n - \frac{1}{n ^{2}}

(D)

1 - \frac{1}{n ^{2}}

Solution

Just take

\frac{1 ( n - 1 ) + ( 1 - \frac{1}{n} )}{n}

. You get

\frac{n - 1 + 1 - \frac{1}{n}}{n}

, which is just

\frac{n - \frac{1}{n}}{n}

, which is just

1 - \frac{1}{n ^{2}}

Final answer

D