If frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The harmonic mean $(HM)$ of two numbers $a$ and $b$ is given by $\frac{2ab}{a + b}$.Given that $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} = \frac{2a

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(B) The harmonic mean $(HM)$ of two numbers $a$ and $b$ is given by $\frac{2ab}{a + b}$.Given that $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} = \frac{2ab}{a + b}$.Cross-multiplying,we get $(a^{n + 1} + b^{n + 1})(a + b) = 2ab(a^n + b^n)$.Expanding both sides: $a^{n + 2} + a^{n + 1}b + ab^{n + 1} + b^{n + 2} = 2a^{n + 1}b + 2ab^{n + 1}$.Rearranging the terms: $a^{n + 2} + b^{n + 2} = a^{n + 1}b + ab^{n + 1}$.$a^{n + 1}(a - b) - b^{n + 1}(a - b) = 0$.$(a^{n + 1} - b^{n + 1})(a - b) = 0$.Since $a 
eq b$,we must have $a^{n + 1} = b^{n + 1}$.This implies $(\frac{a}{b})^{n + 1} = 1 = (\frac{a}{b})^0$.Therefore,$n + 1 = 0$,which gives $n = -1$.

If $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n}$ is the harmonic mean between $a$ and $b$,then the value of $n$ is

Similar Questions

$8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be (in $\sqrt{2}$)

If $a, b, c, d, e$ are in $A.P.$,then the value of $a + b + 4c - 4d + e$ in terms of $a$,if possible,is:

Let $S_k = \frac{1 + 2 + 3 + .... + k}{k}$. If $S_1^2 + S_2^2 + ....... + S_{10}^2 = \frac{5}{12}A$,then $A$ is equal to

The sum $\sum\limits_{k = 1}^{20} {\frac{k}{{{2^k}}}}$ is equal to

Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module