Question
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Answer (Detailed Solution Below)
Option 4 : $\\frac{4}{9}$ / $\\frac{4}{9}$
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Detailed Solution
सही उत्तर $\\frac{4}{9}$ / $\\frac{4}{9}$ है।
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prepsnap.in • Part -AQuestion:
Evaluate: $\\frac{1}{1 \\times 3} + \\frac{1}{3 \\times 5} + \\frac{1}{5 \\times 7} + \\frac{1}{7 \\times 9}$. / मान ज्ञात कीजिए: $\\frac{1}{1 \\times 3} + \\frac{1}{3 \\times 5} + \\frac{1}{5 \\times 7} + \\frac{1}{7 \\times 9}$।
1.
$\\frac{8}{9}$ / $\\frac{8}{9}$
2.
$\\frac{1}{2}$ / $\\frac{1}{2}$
3.
$\\frac{5}{9}$ / $\\frac{5}{9}$
4.
$\\frac{4}{9}$ / $\\frac{4}{9}$
Correct Answer: $\\frac{4}{9}$ / $\\frac{4}{9}$
Each term telescopes: $\\frac{1}{(2n-1)(2n+1)} = \\frac{1}{2}\\left(\\frac{1}{2n-1} - \\frac{1}{2n+1}\\right)$. Sum $= \\frac{1}{2}\\left(1 - \\frac{1}{9}\\right) = \\frac{4}{9}$. / प्रत्येक पद दूरबीन-श्रेणी बनाता है: $\\frac{1}{(2n-1)(2n+1)} = \\frac{1}{2}\\left(\\frac{1}{2n-1} - \\frac{1}{2n+1}\\right)$। योग $= \\frac{1}{2}\\left(1 - \\frac{1}{9}\\right) = \\frac{4}{9}$।
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