Question
Download Solution PDFश्रृंखला \(3 - 1 + \frac{1}{3} - \frac{1}{9} + \ldots \) का योग किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
यदि a, ar, ar2, …. एक अनंत GP है तो अनंत गुणोत्तर श्रृंखला का योग निम्न द्वारा दिया जाता है।
अनंत GP का योग = \({s_\infty } = \;\frac{a}{{1\; - \;r}}\); |r| < 1
गणना:
यहां, हमें श्रृंखला \(3 - 1 + \frac{1}{3} - \frac{1}{9} + \ldots \) का योग खोजना होगा
जैसा कि हम देख सकते हैं कि अनुक्रम a = 3 और r = - 1/3 के साथ एक GP है
श्रृंखला का योग = S∞ = a/ (1 - r)
श्रृंखला का योग = \(\frac{3}{{1\; - \;\frac{{ - 1}}{3}}} = \;\frac{3}{{1 + \;\frac{1}{3}}} = \;\frac{3}{{\left( {\frac{4}{3}} \right)}} = \;\frac{9}{4}\)Last updated on May 30, 2025
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