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jmc

prealgebra junior

Problem

What is the value of the product

(1 + \frac{1}{1}) \cdot (1 + \frac{1}{2}) \cdot (1 + \frac{1}{3}) \cdot (1 + \frac{1}{4}) \cdot (1 + \frac{1}{5}) \cdot (1 + \frac{1}{6}) ?

(A)

\frac{7}{6}

(B)

\frac{4}{3}

(C)

\frac{7}{2}

(D)

7

Solution

By adding up the numbers in each of the

6

parentheses, we get:

\frac{2}{1} \cdot \frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5} \cdot \frac{7}{6}

. Using telescoping, most of the terms cancel out diagonally. We are left with

\frac{7}{1}

which is equivalent to

7

. Thus, the answer would be

7

.

Final answer

D