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If a (1/b+1/c),b(1/c+1/a),c(1/a+1/b) are...

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

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A N EXCEL PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)(xne0) then show that a,b,...

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  2. Let S be the sum P the product and R the sum of reciprocals of n terms...

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  3. The p^(th),q^(th)and r^(th) terms of an A.P. are a,b,c respectively. S...

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

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

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  6. If a and b are the roots of x^2-3x+p=0 and c,d are the roots of x^2-12...

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

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  8. Find sum of 5 + 55 + 555 + ... to n terms.

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  9. Find the sum of the following series upto n terms 0.6+0.66+0.666+…

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  10. Find the 20^(th) term of the series 2xx4+4xx6+6xx8+… to n terms

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  11. Find the sum of the 1^(st) n terms of the series 3+7+13+21+31+…

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  12. If S1.S2.S3 are the sum of the first n natural numbers, their squares ...

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  13. Find the sum of the following series upto n terms (1^3)/1+(1^3+2^3)/(1...

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  14. Show that (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n...

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  15. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

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  16. Shamshad Ali buys a Scooter for Rs. 22000. He pays Rs. 4000 cash and a...

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  17. A person writes a letter to four of his friends. He asks each one of t...

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  18. A man deposited Rs. 10000 in a bank at the rate of 5% simple interest ...

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  19. A manufacturer reckons that the value of a machine, which costs him Rs...

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  20. 150 workers were engaged to finish a job in a certain number of days. ...

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