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If a ,b ,c in R+ form an A.P., then pro...

If `a ,b ,c in R+` form an A.P., then prove that `a+1//(b c),b+1//(a c),c+1//(a b)` are also in A.P.

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a,b,c are in A.P.
`rArr1/(bc),1/(ca),1/(ab)` are also in A.P [Dividing by abc]
`rArra+1/(bc),b+1/(ca),c+1/(ab)` will also be in A.P.
`[because` Sum of two A.P.'s is also an A.P]
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CENGAGE-PROGRESSION AND SERIES-Examples
  1. If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in intege...

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

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  3. If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(a c),...

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  4. If a,b,c are in A.P., then prove that the following are also in A.P ...

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  5. If the sum of three numbers in A.P., is 24 and their product is 440, f...

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  6. Divide 32 into four parts which are in A.P. such that the ratio of the...

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  7. The digits of a positive integer, having three digits, are in A.P. and...

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  8. If eleven A.M. s are inserted between 28 and 10, then find the number ...

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  9. Between 1 and 31, m numbers have been inserted in such a way that the ...

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  10. Find the sum of all three-digit natural numbers, which are divisible b...

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  11. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  12. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))(1+x^(101))dot

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  13. Find the sum of first 24 terms of the A.P. a1, a2, a3, , if it is kno...

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  14. If S1 is the sum of an AP of 'n' odd number of terms and S2 be the sum...

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  15. If the sequence a(1),a(2),a(3),…,a(n) is an A.P., then prove that a(1)...

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  16. If the arithmetic progression whose common difference is nonzero the ...

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  17. The sums of n terms of two arithmetic progressions are in the ratio 5n...

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  18. If n arithmetic means are inserted between 2 and 38, then the sum of t...

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  19. The third term of a geometric progression is 4. Then find the product ...

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  20. The first term of a G.P. is 1. The sum of the third term and fifth ter...

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