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If Sigma(r=1)^(n) r(r+1)(2r +3)=an^4+bn...

If `Sigma_(r=1)^(n) r(r+1)(2r +3)=an^4+bn^3+cn^2+dn +e ` then

A

a-b=d-c

B

e=0

C

`a,b-2//3,c-1 " are in " in A.P`

D

`(b+d)//a` is an integer

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The correct Answer is:
A, B, C, D
`an^(4)+bn^(3)+cn^(3)+dn+e`
`=2sum_(r=1)^(n)r(r+1)(r+2)-sum_(r=1)^(n)r(r+1)`
`=2/4n(n+1)(n+2)(n+3)-1/3n(n+1)(n+2)`
`=1/6(3n^(4)+16n^(3)+27n^(2)+14n)`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Multiple & Comprehension)
  1. For 0 lt phi lt pi//2 , if x =Sigma(n=0)^(oo) cos^(2n) phi ,y=Sigma(n...

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  2. For the series, S=1 +(1)/(1+3)(1+2)^2+(1)/((1+3+5))(1+2+3)^2+(1)/((1...

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  3. If Sigma(r=1)^(n) r(r+1)(2r +3)=an^4+bn^3+cn^2+dn +e then

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  4. If Sn=1^2-2^2+3^2-4^2+5^2-6^2+ ,t h e n S(40)=-820 b. S(2n)> S(2n+2) ...

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  5. 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+ n terms ...

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  6. 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 whe...

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  7. If a, b and c are in H.P., then the value of ((ac+ab-bc)(ab+bc-ac))/(a...

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  8. If p,q and r are in A.P then which of the following is / are true ?

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  9. If x^2+9y^2+25 z^2=x y z((15)/2+5/y+3/z),t h e n x ,y ,a n dz are in ...

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  10. If A1, A2, G1, G2, ; a n dH1, H2 are two arithmetic, geometric and har...

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  11. If 1/(b-a)+1/(b-c)=1/a+1/c , then a ,b ,a n dc are in H.P. a ,b ,a n d...

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  12. If a,b,c are three distinct numbers in G.P., b,c,a are in A.P and a,bc...

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  13. If a,b,c are in A.P and a^2,b^2,c^2 are in H.P then which is of the fo...

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  14. If first and (2n-1)^(th) terms of A.P., G.P. and H.P. are equal and th...

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  15. Let E=1/(1^2)+1/(2^2)+1/(3^2)+ Then, E<3 b. E >3//2 c. E >2 d. E<2

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  16. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

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  17. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

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  18. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

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  19. Consider three distinct real numbers a,b,c in a G.P with a^2+b^2+c^2=t...

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  20. Consider three distinct real numbers a,b,c in a G.P with a^2+b^2+c^2=t...

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