For what value of m- a m-1 - b m-1 a m - b m is the arithmetic mean of -a- and -b- -

The correct option is B 0 According to the question, a ^ m+1 + b ^ m+1 a ^ m + b ^ m = a+b 2 It will satisfy only when m=0 ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

For what valu...

Question

For what value of $m, \frac{a^{m + 1} + b^{m + 1}}{a^{m} + b^{m}}$ is the arithmetic mean of $^{'} a^{'}$ and $^{'} b^{'}$ ?

1

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None of these

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Solution

The correct option is B $0$
According to the question,
$\frac{a^{m + 1} + b^{m + 1}}{a^{m} + b^{m}} = \frac{a + b}{2}$
It will satisfy only when $m = 0$

Suggest Corrections

Similar questions

Q. Show that:

\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

We are giving the concept of A.M of

m^{t h}

power.Let

a, b > 0

and

a \neq b

and let

m

be a real number. Then

\frac{a^{m} + b^{m}}{2} > {(\frac{a + b}{2})}^{m}

m \in R - [0, 1]

However, if

m \in (0, 1)

then

\frac{a^{m} + b^{m}}{2} < {(\frac{a + b}{2})}^{m}

.
Obviously, if

m \in {0, 1}

then

\frac{a^{m} + b^{m}}{2} = {(\frac{a + b}{2})}^{m}

.
On the basis of the above information, answer the following questions:

a

and

b

are positive

(a \neq b)

and

a + b = 1

and if

A = {(a + \frac{1}{a})}^{2} + {(b + \frac{1}{b})}^{2},

then the correct statement is:

Q. Given

x = \frac{b m - 2}{a m - 3}

find

^{'} m^{'},

a = 5, b = 4

and

x = 1

Q. If

a

and

b

are non-zero integers,

m

and

n

are any integers, then which of the following are true?

We are giving the concept of A.M of

m^{t h}

power.Let

a, b > 0

and

a \neq b

and let

m

be a real number. Then

\frac{a^{m} + b^{m}}{2} > {(\frac{a + b}{2})}^{m}

m \in R - [0, 1]

However, if

m \in (0, 1)

then

\frac{a^{m} + b^{m}}{2} < {(\frac{a + b}{2})}^{m}

.
Obviously, if

m \in {0, 1}

then

\frac{a^{m} + b^{m}}{2} = {(\frac{a + b}{2})}^{m}

.
On the basis of the above information, answer the following questions:

The correct statement for sequence

C

is:

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For what value of m,am+1+bm+1am+bm is the arithmetic mean of ′a′ and ′b′ ?

The correct option is B 0According to the question,am+1+bm+1am+bm=a+b2It will satisfy only when m=0

For what value of $m, \frac{a^{m + 1} + b^{m + 1}}{a^{m} + b^{m}}$ is the arithmetic mean of $^{'} a^{'}$ and $^{'} b^{'}$ ?

The correct option is B $0$
According to the question,
$\frac{a^{m + 1} + b^{m + 1}}{a^{m} + b^{m}} = \frac{a + b}{2}$
It will satisfy only when $m = 0$