11TH•Mathematics•Sequences And Series•Exercise 6.7

6.7 Geometric Series

quizQuestion 1 of 6(Total 6 Questions in Exercise)

Find the sum of first 15 terms of the G.P., $1,\ \dfrac{1}{3},\ \dfrac{1}{9},\ \ldots$ .

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Question 1

verifiedVerified Answer

G.P.: (1,\ \dfrac{1}{3},\ \dfrac{1}{9},\ \ldots) (a=1), (r=\dfrac{1}{3}), (n=15) [ S_{15} = \dfrac{1-\left(\dfrac{1}{3}\right)^{15}}{1-\dfrac{1}{3}} = \dfrac{3}{2}\left(1-\dfrac{1}{3^{15}}\right) ] Answer: (\dfrac{3}{2}\left(1-\dfrac{1}{3^{15}}\right))

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