Question
Download Solution PDFनिम्न गुणोत्तर श्रेणी का योगफल ज्ञात कीजिए।
2/5, 2/25, 2/125, 2/625,... n पदों तक
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
2/5, 2/25, 2/125, 2/625,... n पदों तक
प्रयुक्त सूत्र:
गुणोत्तर श्रेणी के n पदों का योग = a(\(\dfrac{1-r^n}{1-r}\))
जहाँ,
a = प्रथम पद
r = सार्व अनुपात
गणना:
यहाँ, a = 2/5
r = 2/25 ÷ 2/5 = 1/5
n पदों तक योग = a\(\dfrac{1-r^n}{1-r}\)
⇒ योग = (2/5)\(\dfrac{1-(1/5)^n}{1-1/5}\)
⇒ योग = (2/5)\(\dfrac{1-(1/5)^n}{4/5}\)
⇒ योग = (2/5) × (5/4) × [1 - (1/5)n]
⇒ योग = 1/2 × [1 - (1/5)n]
∴ सही उत्तर विकल्प 3 है।
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