Discussion
What is the value of
\[ (1+\frac12)(1+\frac13)(1+\frac14)\cdots(1+\frac1{24}) \;? \]
Answer: C
Write each factor as a fraction: 1 + 1/2 = 3/2, 1 + 1/3 = 4/3, 1 + 1/4 = 5/4, and so on up to 1 + 1/24 = 25/24. The product is
\[ \frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots \]
\[ \cdots\times\frac{25}{24} \]
Each numerator cancels the next denominator, so only the 25 at the end and the 2 at the beginning are left, giving 25/2 = 12.5. So the value is 12.5, option (C). The options 0.5, 10 and 25 do not come from the telescoping product.
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