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यदि (a^(n)+b^(n))/(a^(n-1)+b^(n-1)), a त...

यदि `(a^(n)+b^(n))/(a^(n-1)+b^(n-1)),` a तथा b के मध्य समांतर माध्य हो तो n का मान ज्ञात कीजिए |

Text Solution

Verified by Experts

The correct Answer is:
n=1
According to the given condition, we have
`(a+b)/2=(a^(n)+b^(n))/(a^(n-1)+b^(n-1))`
or `(a+b)(a^(n-1)+b^(n-1))=2(a^(n)+b^(n))`
or `a^(n)+ab^(n-1)+ba^(n-1)+b^(n)=2a^(n)+2b^(n)`
or `ab^(n-1)+a^(n-1)b=a^(n)+b^(n)`
or `ab^(n-1)-b^(n)=a^(n)-a^(n-1)b`
or `b^(n-1)(a-b)=a^(n-1)(a-b)`
or `b^(n-1)=a^(n-1)`
or `(a/b)^(n-1)=1=(a/b)^(0)`
`rArrn-1=0`
or n=1
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