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If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., ...

If `(b-c)^2,(c-a)^2,(a-b)^2` are in A.P., then prove that `1/(b-c),1/(c-a),1/(a-b)` are also in A.P.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
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  2. The fourth, seventh, and the last term of a G.P. are 10, 80, and 2560,...

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  3. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

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  4. If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) ar...

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  5. Let Sn denote the sum of first n terms of an A.P. If S(2n)=3Sn , then ...

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  6. If p ,q ,a n dr are inA.P., show that the pth, qth, and rth terms of a...

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  7. Find four number in an A.P. whose sum is 20 and sum of their squares i...

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  8. Find the sum of the following series : 0. 7+0. 77+0. 777+ ton term...

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  9. Find the sum of the series 1/(3^2+1)+1/(4^2+2)+1/(5^2+3)+1/(6^2+4)+oo

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  10. Prove that in a sequence of numbers 49,4489,444889,44448889 in which e...

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  11. Find the sum of first 100 terms of the series whose general term is ...

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  12. If the continued product o three numbers in a G.P. is 216 and the sum ...

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  13. Find the sum of the series 2/(1xx2)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/...

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  14. The sum of some terms of G. P. is 315 whose first term and the comm...

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  15. A sequence of numbers An, n=1,2,3 is defined as follows : A1=1/2 and f...

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  16. The sum of three numbers in GP. is 56. If we subtract 1, 7, 21 from ...

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  17. Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+...

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  18. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are ...

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  19. Find the sum sum(r=0)^n^(n+r)Cr .

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  20. Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1...

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