Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

Let $t_n = \frac{n(n+1)}{2}$ be the $n$ th triangular number. Find
$\frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + ... + \frac{1}{t_{2002}}$
$\text{(A) }\frac {4003}{2003}$ $\text{(B) }\frac {2001}{1001}$ $\text{(C) }\frac {4004}{2003}$ $\text{(D) }\frac {4001}{2001}$ $\text{(E) }2$

Solution

If $\log_{b} 729 = n$ , then $b^n = 729$ . Since $729 = 3^6$ , $b$ must be $3$ to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of $b \Longrightarrow \boxed{\mathrm{E}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.