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{an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to?
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{an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for...
Explanation:
Given Sequence:
- The given sequence is an infinite sequence {an} where a1=1, a2=1, and an 2=2an 1 an for all n>=1.
Recursive Relation:
- We have the recursive relation an 2 = 2an 1 an for all n>=1.
Finding the Value of an:
- By substituting n=2 in the recursive relation, we get a2 2 = 2a1 a2, which gives a2=2.
- Similarly, continuing this process, we can find the values of an for all n>=1.
Calculating the Sum:
- We need to find the value of 47∑n=1 an/8^n as n tends to infinity.
Convergence of the Series:
- As per the given recursive relation, the sequence {an} is well-defined and converges.
- We can find the limit of an as n tends to infinity and then calculate the sum of the series.
Limit Calculation:
- By finding the limit of an as n tends to infinity, we can determine the value of the series sum.
Final Answer:
- The final value of 47∑n=1 an/8^n as n tends to infinity can be calculated using the limits of the sequence {an}.
This analysis provides a detailed explanation of how to approach the given problem and calculate the required sum as n tends to infinity.
Given Sequence:
- The given sequence is an infinite sequence {an} where a1=1, a2=1, and an 2=2an 1 an for all n>=1.
Recursive Relation:
- We have the recursive relation an 2 = 2an 1 an for all n>=1.
Finding the Value of an:
- By substituting n=2 in the recursive relation, we get a2 2 = 2a1 a2, which gives a2=2.
- Similarly, continuing this process, we can find the values of an for all n>=1.
Calculating the Sum:
- We need to find the value of 47∑n=1 an/8^n as n tends to infinity.
Convergence of the Series:
- As per the given recursive relation, the sequence {an} is well-defined and converges.
- We can find the limit of an as n tends to infinity and then calculate the sum of the series.
Limit Calculation:
- By finding the limit of an as n tends to infinity, we can determine the value of the series sum.
Final Answer:
- The final value of 47∑n=1 an/8^n as n tends to infinity can be calculated using the limits of the sequence {an}.
This analysis provides a detailed explanation of how to approach the given problem and calculate the required sum as n tends to infinity.
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{an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to?
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{an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about {an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for {an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to?.
{an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about {an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for {an}^infinity n=1 be a sequence such that a1=1, a2=1 an 2=2an 1 an for all n>=1 then the value of 47summation n=1 tend to infinity an/8^n is equal to?.
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