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The HCF of x^(2) - y^(2), x^(3) - y^(3),...

The HCF of `x^(2) - y^(2), x^(3) - y^(3), …... x^(n) - y^(n)`, where `n in N` is ………. .

A

`x-y`

B

`x+y`

C

`x^(n)-y^(n)`

D

do not intersect

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The sum of first n terms of the series 1 + (1 + x) y+ (1 + x + x^(2)) y^(2) + (1 + x + x^(2) + x^(3))y^(3) + ……….. is

    A
    `(1/(1 - x))[(1-y^(n))/(1 - y) - y ((1 - x^(n)y^(n))/(1 - xy))]`
    B
    `(1/(1 - x))[(1-y^(n))/(1 - y^(2)) - x ((1 - x^(n)y^(n))/(1 - xy))]`
    C
    `(1/(1 - x))[(1-y^(n))/(1 - y) - x^(2) ((1 - x^(n)y^(n))/(1 - xy))]`
    D
    `(1/(1 - x))[(1-y^(n))/(1 - y) - 2x ((1 - x^(n)y^(n))/(1 - xy))]`

  • The value of n for which the expression (x^(n + 1) + y^(n + 1))/(x^(n) + y^(n)) is arithmetic mean between x and y is

    A
    0
    B
    1
    C
    `-1`
    D
    2

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