A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- If in an HP, tm=n and tn=m then prove that t(m+n)=(mn)/(m+n).
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- The sum of three consecutive terms in H.P is 37 and the sum of their r...
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- If pth, qth and rth terms of a HP be respectivelya,b and c, has prove ...
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- 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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- (i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c)...
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- If b is the harmonic mean between a and c, then prove that 1/(b-a)+...
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- 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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- If log(a+c)+log(a+c-2b)=2log(a-c) then
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- If a, b, c, d be in H.P. then prove that ab + bc+cd =3ad
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- If x1,x2,x3….,xn are in H.P. prove that x1x2+x2x3+x3x4+……….+x(n-1)xn=(...
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- If (b +c), (c + a), (a+ b) are in H. P. then prove that a/(b+c) , b...
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- If (x+y)/(2),y,(y+z)/(2) are in HP, then x,y, z are in
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- If a, b, c, d be four numbers of which the first three are in AP and t...
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- Suppose a is a fixed real number such that (a - x)/(px) = (a - y)/(qy)...
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- 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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- If three numbers are in G.P., then the numbers obtained by adding the ...
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- If a, b, c, are both in G.P. and H.P., Tp= 0, Tq = b, Tr= C, then a (...
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- 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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- If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then p...
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- a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove...
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