1989 USAMO Problems/Problem 1

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Problem

For each positive integer $n$, let

$S_n = 1 + \frac 12 + \frac 13 + \cdots + \frac 1n$

$T_n = S_1 + S_2 + S_3 + \cdots + S_n$

$U_n = \frac{T_1}{2} + \frac{T_2}{3} + \frac{T_3}{4} + \cdots + \frac{T_n}{n+1}$.

Find, with proof, integers $0 < a,\ b,\ c,\ d < 1000000$ such that $\displaystyle T_{1988} = a S_{1989} - b$ and $\displaystyle U_{1988} = c S_{1989} - d$.

Solution

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See also

1989 USAMO (ProblemsResources)
Preceded by
First question
Followed by
Problem 2
1 2 3 4 5
All USAMO Problems and Solutions
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