Question
Download Solution PDFFind the sum of the G.P. :
4/5 , 4/25 , 4/125 , 4/625 ,... to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Series is 4/5 , 4/25 , 4/125 , 4/625 ,... to n term
Formula used:
Sum = a (1 - rn) / (1 - r )
Where a = first term & r = common difference
Calculation:
Common difference (r) = (4/25) ÷ (4/5)
⇒ (1/5)
Putting the value of r in the above formula we get:
Sum = \(\frac{4}{5}\)(1 - \(\frac{1}{5}\)n) / 1 - \(\frac{1}{5}\)
⇒ \(\frac{4}{5}\)(1- (\(\frac{1}{5}\))n) / \(\frac{4}{5}\)
⇒ (1 - (\(\frac{1}{5}\))n)
Hence the correct answer is "(1 - (\(\frac{1}{5}\))n)".
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