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in Geometric Progressions by (15.7k points)

Find the sum of the GP : 

1 - \(\frac{1}{2} + \frac{1}{4}\) = \(\frac{1}{8}\) +. .. to 9 terms

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1 Answer

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by (15.2k points)

Sum of a G.P. series is represented by the formula, Sn = a\(\frac{1-r^n}{1-r}\) , when |r|<1. 

‘Sn’ represents the sum of the G.P. series up to nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms. 

Here, 

a = 1 

r = (ratio between the n term and n-1 term) -\(\frac{1}{2} \div 1 = -\frac{1}{2}\)

n = 9 terms

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