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If in an HP, tm=n and tn=m then prove th...

If in an HP, `t_m=n` and `t_n=m` then prove that `t_(m+n)=(mn)/(m+n)`.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. Find a three digit numberwhose consecutive digits form a GP. If we sub...

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  2. If the number 1/(k+2),1/k^2 and 1/(4k+5) are three consecutiv terms of...

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  3. If in an HP, tm=n and tn=m then prove that t(m+n)=(mn)/(m+n).

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  4. The sum of three consecutive terms in H.P is 37 and the sum of their r...

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  5. If pth, qth and rth terms of a HP be respectivelya,b and c, has prove ...

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  6. 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 ,...

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  7. (i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c)...

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  8. If b is the harmonic mean between a and c, then prove that 1/(b-a)+...

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  9. If a, b, c are in HP then prove that b^2(a-c)^2=2{c^2(b-a)^2+a^2(c-b)...

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  10. If log(a+c)+log(a+c-2b)=2log(a-c) then

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  11. If a, b, c, d be in H.P. then prove that ab + bc+cd =3ad

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  12. If x1,x2,x3….,xn are in H.P. prove that x1x2+x2x3+x3x4+……….+x(n-1)xn=(...

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  13. If (b +c), (c + a), (a+ b) are in H. P. then prove that a/(b+c) , b...

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  14. If (x+y)/(2),y,(y+z)/(2) are in HP, then x,y, z are in

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  15. If a, b, c, d be four numbers of which the first three are in AP and t...

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  16. Suppose a is a fixed real number such that (a - x)/(px) = (a - y)/(qy)...

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  17. If a,b,c,d be in G.P. and a^x=b^y=c^z=d^w, prove that 1/x,1/y,1/z,1/w ...

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  18. If three numbers are in G.P., then the numbers obtained by adding the ...

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  19. If a, b, c, are both in G.P. and H.P., Tp= 0, Tq = b, Tr= C, then a (...

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  20. If a,b,c,d,e be 5 numbers such that a,b,c are in A.P; b,c,d are in GP ...

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