Question
Download Solution PDFमान लीजिए a, b, c समांतर श्रेणी में हैं, तो 1/ab, 1/ca और 1/bc किसमें हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि a,b, c समांतर श्रेणी में हैं, तो 2b = a + c या b - a = c - b है।
गणना:
दिया गया है: a, b, c समांतर श्रेणी में हैं
माना कि 1/ab, 1/ca और 1/bc समांतर श्रेणी में हैं।
⇒\(\rm \frac{1}{ca}\rm -\frac{1}{ab}=\rm \frac{1}{bc}-\rm \frac{1}{ca}\)
\(\rm \frac{1}{a}( \frac{1}{c}- \frac{1}{b})= \frac{1}{c}( \frac{1}{b}- \frac{1}{a})\\ ⇒ \frac{b-c}{abc}= \frac{a-b}{abc}\)
⇒ b - c = a - b
⇒2b = a + c
⇒ a,b, c समांतर श्रेणी में हैं, जो सत्य है।
Last updated on May 30, 2025
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