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(i) a , b, c are in H.P. , show that (b...

(i) a , b, c are in H.P. , show that ` (b + a)/(b -a) + (b + c)/(b - c) = 2 `
(ii) If ` a^(2), b^(2), c^(2) ` are A.P. then b + c , c + a , a + b are in H.P. .

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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. If a,b,c,d are in H.P., then ab+bc+cd is equal to

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  2. The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is 50(1-i) b. 2...

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  3. (i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c)...

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  4. If a,b,c are in H.P, then

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  5. If a , b, c, be in A.P. , b, c,d in G.P. and c.d.e.in H.P., then prov...

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  6. If (a+b)/(1-ab),b,(b+c)/(1-bc) are in AP, then a,(1)/(b),c are in

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  7. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

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  8. Sum of the first p, q and r terms of an A.P are a, b and c, respectiv...

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  9. If Sn=1/1^3 +(1+2)/(1^3+2^3)+...+(1+2+3+...+n)/(1^3+2^3+3^3+...+n^3) T...

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  10. If a,b and c are in A.P. a,x,b are in G.P. whereas b, y and c are also...

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  11. If log(x+z)+log(x-2y+z)=2log(x-z)," then "x,y,z are in

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  12. If (1)/(a)+(1)/(c)+(1)/(a-b)+(1)/(c-b)=0, than prove that a,b,c are in...

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  13. If arithmetic mean of two positive numbers is A, their geometric mean ...

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  14. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

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  15. If a, b, c are in G.P, then loga x, logb x, logc x are in

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  16. If the sum of series 1+(3)/(x)+(9)/(x^(2))+(27)/(x^(3))+ . . .. " to "...

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  17. If H be the H.M. between a and b, then the value of (H)/(a)+(H)/(b) is

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  18. The sum of n terms of two arithmetic progressions are in the ratio 2n+...

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  19. If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)...

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  20. Show that X^((1)/(2))*X^((1)/(4))*X^((1)/(8))... Upto oo = X

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