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Prove that {:((666 ….6)^2+(888….8)=4444…...

Prove that `{:((666 ….6)^2+(888….8)=4444…..4),(" ""n digits " " n digits " " 2n digits "):}`

A

`(4)/(9)(10^(n)-1)`

B

`(4)/(9)(10^(2n)-1)`

C

`(4)/(9)(10^(n)-1)^(2)`

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. For a sequence {a(n)}, a(1) = 2 and (a(n+1))/(a(n)) = 1/3, Then unders...

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  2. In an arithmetic sequence a(1),a(2),a(3), . . . . .,a(n), Delta=|{:(...

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  3. Prove that {:((666 ….6)^2+(888….8)=4444…..4),(" ""n digits " " ...

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  4. Thr ciefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)"…."(x-n),...

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  5. The sum of the series 1^(2)+1+2^(2)+2+3^(2)+3+ . . . . .. +n^(2)+n, is

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  6. If H1. H2...., Hn are n harmonic means between a and b(!=a), then the ...

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  7. If a,b,c be respectively the p^(th),q^(th)andr^(th) terms of a H.P., ...

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  8. If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove ...

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  9. The cubes of the natural numbers are grouped as 1^(3),(2^(3),3^(3)),(4...

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  10. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

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  11. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

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  12. If a ,b ,c ,d ,e ,f are A.M.s between 2 and 12, then find the sum a+b+...

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

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  14. If x,y,z are in H.P then the value of expression log(x+z)+log(x-2y+z)=

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

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

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

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

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