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If an + bn/an - 1 + bn - 1 is the A.M between a and b , then find the value of n

Solution:

A.M of a and b = (a + b)/2

According to the question,

⇒ (a + b)/2 = (an + bn)/(an - 1 + bn - 1)

⇒ (a + b)(an - 1 + bn - 1)

= 2 (an + bn)

⇒ an + abn - 1 + ban - 1 + bn = 2an + 2bn

⇒ abn - 1 + ban - 1 = an + bn

⇒ abn - 1 - bn = an - ban - 1

⇒ bn - 1 (a - b) = an - 1 (a - b)

⇒ bn - 1= an - 1

(a/b)n - 1 = 1 = (a/b)(a/b)0

⇒ n - 1 = 0

⇒ n = 1

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.2 Question 15

If an + bn/an - 1 + bn - 1 is the A.M between a and b , then find the value of n

Summary:

The value of n given that an + bn/an - 1 + bn - 1 is the A.M between a and b is 1

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