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Easy

Question

If A_r = $open parentheses table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close parentheses$ where r is a natural number then |A₁| + |A₂| + |A₃| + ......+ |A₂₀₀₆| mustbe equal to

2006
(2006)²
(2006)³
2007

The correct answer is: (2006)²

|A_r| = r² –(r –1)² = 2r –1
$rightwards double arrow$ |A₁| + |A₂| + ...... + |A₂₀₀₆|
= $not stretchy sum subscript r equals 1 end subscript superscript 2006 end superscript left parenthesis 2 r minus 1 right parenthesis$ = (2006)²

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