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  4. The expression (1+3+5+ ldots+99/2+4+6+ ldots .+100) when simplified, reduces to the fraction

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Q. The expression $\frac{1+3+5+\ldots+99}{2+4+6+\ldots .+100}$ when simplified, reduces to the fraction

Sequences and Series

Solution:

$S _{ N }=50^{2} ; S _{ D }=\frac{2 \cdot 50 \cdot 51}{2}=50 \cdot 51$
$\Rightarrow \frac{ N }{ D }=\frac{50}{51}$