Find the sum of the G.P.:

5/4,5/16,5/64,5/256, to n terms.

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  1. (1(1/4n))
  2. 3/5(1(1/4n))
  3. 2/3(1(1/4n))

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Detailed Solution

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Given:

G.P. series: 5/4, 5/16, 5/64, 5/256, ... up to n terms

Formula used:

Sum of n terms of G.P. = a × (1 - rn) ÷ (1 - r), where |r| < 1

Calculations:

First term (a) = 5/4

Common ratio (r) = (5/16) ÷ (5/4) = 1/4

Sum = (5/4) × (1 - (1/4)n) ÷ (1 - 1/4)

= (5/4) × (1 - (1/4)n) ÷ (3/4)

= (5/4) × (4/3) × (1 - (1/4)n)

= (5/3) × (1 - (1/4)n)

∴ Sum of n terms = (5/3) × (1 - (1/4)n)

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