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Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a?
Most Upvoted Answer
Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1)...
Given Equation:
Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60
Finding the value of a:
To find the value of 'a', we need to simplify the given limit expression.
Using Limit Properties:
As n tends to infinity, the expression can be simplified using the properties of limits.
Applying Limit Definition:
We can rewrite the expression in terms of the limit definition for integration and apply the limit as n tends to infinity.
Applying Limit Laws:
By applying limit laws and simplifying the expression, we can equate it to the given value of 1/60.
Solving for 'a':
By solving the simplified expression and equating it to 1/60, we can find the value of 'a'.
Final Answer:
The value of 'a' obtained from the calculation will satisfy the given limit equation.
Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60
Finding the value of a:
To find the value of 'a', we need to simplify the given limit expression.
Using Limit Properties:
As n tends to infinity, the expression can be simplified using the properties of limits.
Applying Limit Definition:
We can rewrite the expression in terms of the limit definition for integration and apply the limit as n tends to infinity.
Applying Limit Laws:
By applying limit laws and simplifying the expression, we can equate it to the given value of 1/60.
Solving for 'a':
By solving the simplified expression and equating it to 1/60, we can find the value of 'a'.
Final Answer:
The value of 'a' obtained from the calculation will satisfy the given limit equation.
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Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a?
Question Description
Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a?.
Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lim x tends to infinite (1^a +2^a +3^a+ ...+ n^a)/(n+ 1)^(a-1)((na +1) +(na+ 2) +...(na+ n))=1/60 Then find the value of a?.
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