JEE Exam > JEE Questions > {an}^infinity n=1 be a sequence such that a1=...
Start Learning for Free
{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?
Most Upvoted Answer
{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.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
{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?
Question Description
{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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of {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? defined & explained in the simplest way possible. Besides giving the explanation of
{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?, a detailed solution 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? has been provided alongside types of {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? theory, EduRev gives you an
ample number of questions to practice {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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup