निम्न गुणोत्तर श्रेढ़ी का योगफल ज्ञात कीजिए।

11/5, 11/25, 11/125, 11/625 , ... n पदों तक

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  1. 2/5(1-(1/5)n)
  2. 11/4(1-(1/5)n)
  3. 11/5(1-(1/5)n)
  4. 4/11(1-(1/5)n)

Answer (Detailed Solution Below)

Option 2 : 11/4(1-(1/5)n)
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दिया गया है:

11/5, 11/25, 11/125, 11/625 , ...  n पदों तक

प्रयुक्त सूत्र:

योगफल = a (1 - rn) / (1 - r )

जहाँ a = पहला पद और r = सार्व अनुपात

गणना:

सार्व अनुपात (r) = (11/25) ÷ (11/5)

⇒ (1/5)

उपरोक्त सूत्र में r का मान रखने पर हमें प्राप्त होता है:

योगफल = \(\frac{11}{5}\)(1 - \(\frac{1}{5}\)n) / 1 - \(\frac{1}{5}\)

⇒ \(\frac{11}{5}\)(1- (\(\frac{1}{5}\))n) / \(\frac{4}{5}\)

⇒ \(\frac{11}{4}\)(1 - (\(\frac{1}{5}\))n)

अतः सही उत्तर  "​​​\(\frac{11}{4}\)(1 - (​\(\frac{1}{5}\))n)" है।

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