Question
Download Solution PDFFind the sum of the G.P.:
5/11, 5/121, 5/1331, 5/14641, ... to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
G.P. = 5/11, 5/121, 5/1331, 5/14641, ... up to n terms
Formula used:
G.P. sum to n terms = a × (1 - rn) / (1 - r)
First term (a) = 5/11
Common ratio (r) = (5/121) ÷ (5/11) = 1/11
Calculations:
Sum = (5/11) × [1 - (1/11)n] / (1 - 1/11)
⇒ Sum = (5/11) × [1 - (1/11)n] / (10/11)
⇒ Sum = (5/11) × (11/10) × [1 - (1/11)n]
⇒ Sum = (5/10) × [1 - (1/11)n] = (1/2) × [1 - (1/11)n]
∴ Sum to n terms = (1/2) × [1 - (1/11)n]
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