Question
Download Solution PDF1/1.5 + 1/0.15 + 1/0.015 + ... = 74074074 श्रेणी में कितने पद हैं ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
श्रेणी: 1/1.5 + 1/0.15 + 1/0.015 + ... = 74074074
प्रयुक्त सूत्र:
गुणोत्तर श्रेढ़ी (GP) का योग = a(1 - rn) / (1 - r),
गणना:
दिया गया है, 2/3 + 20/3 + 200/3 + ... = 74074074
यहाँ, a = 2/3
r = (20/3) / (2/3) = 10
माना, 'n' पदों की संख्या है।
योग = (2/3)(1 - 10n) / (1 - 10) = 74074074
(2/3)(1 - 10n) / (-9) = 74074074
(2/3)(10n - 1) / 9 = 74074074
2(10n - 1) = 74074074 x 27
10n - 1 = 74074074 × 27 / 2 = 999999999
10n = 1000000000
10n = 109
n = 9
∴ श्रेणी में 9 पद हैं।
Last updated on May 14, 2025
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