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If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c...

If `sum_(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e ,` then (a) `a-b=d-c` (b) `e=0` (c) `a , b-2//3, c-1` are in A.P. (d) `(b+d)//a` is an integer

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  2. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  3. If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca...

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  4. Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3...

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  5. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then find c...

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  6. The 9th term of the series 27+9+52/5+36/7+.... will be (a) 110/17 (b...

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  7. If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

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  8. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then (a) a-b=d-c ...

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  9. If a,b,c,d are in GP then prove thst (b+c)(b+d) =(c+a)(c+d)

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  10. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

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  11. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  12. If in a progression a1, a2, a3,.......... e tc dot,(ar-a(r+1)) bears...

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  13. a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d ar...

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  14. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

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  15. Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....

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  16. If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b :...

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  17. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

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  18. The sum of three numbers in G.P. is 14. If one is added to the first ...

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  19. If x ,2x+2 and 3x+3 are the first three terms of a G.P., then the four...

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  20. The harmonic mean of two numbers is 4. Their arithmetic mean A and the...

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