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If a ,b ,ca n dd are in H.P., then prove...

If `a ,b ,ca n dd` are in H.P., then prove that `(b+c+d)//a ,(c+d+a)//b ,(d+a+b)//c` and `(a+b+c)//d` , are in A.P.

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a,b,c, and d are in H.P.
`rArr1/a,1/b,1/c,1/d` are in A.P.
`rArr(a+b+c+d)/a,(a+b+c+d)/b,(a+b+c+d)/c,(a+b+c+d)/d` are in A.P.
`rArr1+(b+c+d)/a,(a+c+d)/b+1,(a+b+d)/c+1,(a+b+c)/d+1` are in A.P.
`rArr (b+c+d)/a,(a+c+d)/b,(a+b+d)/c,(a+b+c)/d` are in A.P.
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CENGAGE-PROGRESSION AND SERIES-Examples
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  2. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then ...

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  3. If a ,b ,ca n dd are in H.P., then prove that (b+c+d)//a ,(c+d+a)//b ,...

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  4. The mth term of a H.P is n and the nth term is m . Proves that its rth...

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  5. If agt1,bgt1andcgt1 are in G.P., then show that 1/(1+log(e)a),1/(1+log...

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  6. If a,b,c are in G.P and a + x, b +x, c + x are in H.P, then the value ...

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  7. If first three terms of the sequence 1//16 ,a , b , c1//16 are in geom...

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  8. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

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  9. Insert four H.M.s between 2/3 and 2/13.

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  10. If nine arithmetic means and nine harmonic means are inserted between ...

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  11. Let a ,b be positive real numbers. If a A1, A2, b be are in arithmetic...

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  12. The A.M. and H.M. between two numbers are 27 and 122, respectively, ...

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  13. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

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  14. Find the sum 2017+1/4(2016+1/4(2015+…+1/4(2+1/4(1))..))

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  15. The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is give...

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  16. Find the sum to ininity of the series 1-3x+5x^2+7x^3+..... oo when Ix|...

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  17. The sum of the infinite series 1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))...

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  18. If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+oo is (4...

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  19. Find the sum to infinity of the series 1^2+2^2+3^2+4^2+oodot

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  20. Find the sum 2xx5+5xx9+8xx13+11xx17+.. n terms.

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