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If a1,a2,a3, ,an are an A.P. of non-z...

If `a_1,a_2,a_3, ,a_n` are an A.P. of non-zero terms, prove that `1/(a_1+a_2)+1/(a_1+a_3)++1/(a_(n-1)+a_n)=(n-1)/(a_1+a_n)dot`

A

`(a_(1).a_(n))/(2)`

B

`(a_(1).a_(n))/(n)`

C

`(n-1)/(a_(1).a_(n))`

D

`(n)/(a_(1).a_(n))`

Text Solution

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The correct Answer is:
C
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MARVEL PUBLICATION-SEQUENCES AND SERIES -MULTIPLE CHOICE QUESTIONS
  1. let a1,a2,a3,...........,be an AP such that (a1+a2+a3+...........+ap)/...

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  2. If a(1),a(2),a(3),"….",a(n) are in AP, where a(i)gt0 for all I, the va...

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  3. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1+a2...

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  4. If a,b,c are in both : A.P. and G.P. then (A)a=b!=c (B)a!=b=c (C) a!=b...

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  5. If x,y,z are in A.P. then : e^(-x), e^(-y),e^(-z) are in (a) A.P (b) G...

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  6. If x,y,z are in A.P. then : yz,zx,xy are in

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  7. If in a G.P., {a(n)} it given that (a) 120 (b)124 (c) 128 (d) 132

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  8. Every term of a G.P. is positive and also every term is the sum of pre...

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  9. If in a g.P. { t(n)) it is given that t(p+q) =a and t(p-q) = b then :...

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  10. If , in a G.P. {a(n)} it is given that a(1)+a(2)+a(3)+a(4)= 30 ...

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  11. If {a(n)} is a G.P. of positive terms then : (sqrt(a(1)a(2))+sqr...

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  12. The sides of a right angled triangle arein A.P., then they are in the...

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  13. If x,y,z are in G.P and a^x=b^y=c^z,then

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  14. If p^(th),q^(th) and r^(th) terms of an A.P. are in G.P., then the co...

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  15. IF x,2y,3z are in A.P. where x,y,z are unequal number in a G.P., then ...

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  16. If x,2x+2,3x+3 are the first three terms of a GP, then what is its fou...

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  17. If a,b,c,d are positive numbers such that a,b,c are in A.P. and b,c,d ...

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  18. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  19. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

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  20. If a,b,c, are in G.P. , a.x.b in A.P. and b,y,c in A.P., then : (a)/(...

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