Question
Download Solution PDFFind the sum of the G.P.:
2/5, 2/25, 2/125, 2/625,... to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
2/5, 2/25, 2/125, 2/625,... to n terms.
Formula used:
Sum of a G.P. to n terms = a(\(\dfrac{1-r^n}{1-r}\))
Where,
a = first term
r = common ratio
Calculation:
Here, a = 2/5
r = 2/25 ÷ 2/5 = 1/5
Sum to n terms = a\(\dfrac{1-r^n}{1-r}\)
⇒ Sum = (2/5)\(\dfrac{1-(1/5)^n}{1-1/5}\)
⇒ Sum = (2/5)\(\dfrac{1-(1/5)^n}{4/5}\)
⇒ Sum = (2/5) × (5/4) × [1 - (1/5)n]
⇒ Sum = 1/2 × [1 - (1/5)n]
∴ The correct answer is option 3.
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