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a,b,c are in H.P. then prove that (b +a)...

a,b,c are in H.P. then prove that `(b +a)/(b-a) + (b+c)/(b-c) =2`

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RESONANCE-SEQUENCE & SERIES -SELF PRACTICE PROBLEMS
  1. Find the maximum sum of the A.P. 40 +38+36+34+32+……………

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  2. Find the sum of first 16 terms of an A.P. a (1), a (2), a(3)……….. If...

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  3. There are n A.M.'s between 3 and 29 such that 6th mean : (n - 1)th mea...

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  4. For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)),...

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  5. Find the G.P. if the common ratio of G.P. is 3, n^(th) term is 486 an...

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  6. if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...

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  7. A G.P consists of 2n terms . If the sum of the terms . If the sum of ...

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  8. If the continued product of three numbers in G.P. is 216 and the sum o...

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  9. Find the value of n so that (a ^(n +2) + b ^(n +1))/( a ^(n) + b ^(n))...

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  10. If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then ...

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  11. If the harmonic mean between two positive numbers is to their G.M. as ...

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  12. a,b,c are in H.P. then prove that (b +a)/(b-a) + (b+c)/(b-c) =2

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  13. If a,b,c,d are in H.P., then ab+bc+cd is equal to

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  14. If 4 + (4 +d)/( 5) + (4 + 2d)/(5 ^(2)) ……….=1, then find d.

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  15. Evaluate :1 + 3x + 6x ^(2) + 10 x ^(3)+……. upto infinite term, whre |x...

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  16. Sum of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………

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  17. Find the sum to n terms of the series: 3/(1^^2 .2^2)+5/(2^2 .3^2)+7/(3...

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  18. Find the sum to n terms of the series 1+ (1+2) + (1+2+3) + (1+2+ 3+...

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  19. Generate term of the series 4 + 14 + 30 + 52+ 82+ 114+.........

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  20. If sum (r =1) ^(n ) T (r) = (n +1) ( n +2) ( n +3) then find sum ( r ...

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