If x(1), x(2), x(3) .................x(n...

If `x_(1), x_(2), x_(3) .................x_(n)` are in H.P.then `x_(1)x_(2)+x_(2)x_(3)+.......+x_(n-1)x_(n)`=

`(n +1)x_(1)x_(n)`

`(n -1)x_(1)x_(n)`

`nx_(1)x_(n)`

`(n^(2) -1)x_(1)x_(n)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCES AND SERIES
DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos
SEQUENCES AND SERIES
DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos
RELATIONS AND FUNCTIONS-2
DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos
SETS
DISHA PUBLICATION|Exercise EXERCISE-2 : CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

If x_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

Q.if x_(1),x_(2)......x_(n) are in H.P. then sum_(r=1)^(n)x_(r)x_(r+1) is equal to :(A)(n-1)x_(1)x_(n)(B)nx_(1)x_(n)(C)(n+1)x_(1)x_(n)(D)(n+2)x_(1)x_(n)

If x_(1),x_(2),x_(3),.......x_(n) are the roots of x^(n)+ax+b=0, then the value of (x_(1)-x_(2))(x_(1)-x_(3))(x_(1)-x_(4))......(x_(1)x_(n)) is equal to

If x_(1),x_(2),x_(3),"……" are in A.P., then the value of 1/(x_(1)x_(2))+1/(x_(2)x_(3))+1/(x_(3)x_(4))+"……"1/(x_(n-1)x_(n)) is :

If x_(1),x_(2),x_(3),x_(n) are the roots of x^(n)+ax+b=0 then the value of (x_(1)-x_(2))(x_(1)-x_(3))(x_(1)-x_(4))......(x_(1)-x_(n)) is equal to

Each of the numbers x_(1),x_(2),x_(3),...x_(n),n>=4 is equal to 1 or -1. Suppose x_(1)x_(2)x_(3)x_(4)+x_(2)x_(3)x_(4)x_(5)+x_(3)x_(4)x_(5)x_(6)+....x_(n-3)x_(n-2)x_(n-1)x_(n)+x_(n-2)x_(n-1)x_(n)x_(1)+x_(n-1)x then

DISHA PUBLICATION-SEQUENCES AND SERIES -EXERCISE -1 : Concept Builder

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the...
Text Solution
|
Given that alpha,gamma are roots of the equation A x^2-4x+1=0,a n dbet...
Text Solution
|
If x(1), x(2), x(3) .................x(n) are in H.P.then x(1)x(2)+x(2...
Text Solution
|
If the harmonic mean between a and b be H, then the value of 1/(H-a)+...
Text Solution
|
The sum of 0. 2+0004+0. 00006+0. 0000008+... to oo is (200)/(891) b. ...
Text Solution
|
If the p^(th), q^(th) and r^(th) terms of a H.P. are a,b,c respectivel...
Text Solution
|
If a,b,c are three distinct positive real numbers which are in H.P., t...
Text Solution
|
If a,b,c are in H.P., then the value of ((1)/(b)+(1)/(c)-(1)/(a))((1...
Text Solution
|
If the 7^(th) term of a H.P is (1)/(10) and the 12^(th) term is (1)/(2...
Text Solution
|
If 1/1^4+1/2^4+1/3^4+...+oo=pi^4/90, then 1/1^4+1/3^4+1/5^4+...+oo=
Text Solution
|
If x, y and z are pth, gth and rth terms respectively of an A.P and al...
Text Solution
|
The AM, HM and GM between two number are (144)/(15), 15 and 12, but no...
Text Solution
|
If a1, a2, a3, an are in H.P. and f(k)=(sum(r=1)^n ar)-ak ,t h e n (a...
Text Solution
|
If the p^(th), q^(th) and r^(th) terms of a GP. Are again in G.P., the...
Text Solution
|
If x gt 0, (x^(n))/(1+x+x^(2)+...+x^(2n)) is
Text Solution
|
If a + b + c = 3 and a > 0, b>0,c>0 the greatest value of a^2b^3c^2
Text Solution
|
If 1/(b-a)+1/(b-c)=1/a+1/c , then a,b,c are in (A) AP (B) GP (C) ...
Text Solution
|
If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...
Text Solution
|
If A and G be the AM and GM between two positive no.'s ; then the numb...
Text Solution
|
Consider the sequence of numbers 121, 12321, 1234321,... Each term in ...
Text Solution
|