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in Geometric Progressions by (15.7k points)

Find the sum of the GP :

1 - \(\frac{1}{3}\) + \(\frac{1}{3^2}\) - \(\frac{1}{3^3}\) + ..... to n 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) -\(\frac{1}{3} \div 1 = -\frac{1}{3}\)

n terms

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