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If Sigma(r=1)^(n) r^4=I(n), " then "Sigm...

If `Sigma_(r=1)^(n) r^4=I(n), " then "Sigma__(r=1)^(n) (2r -1)^4` is equal to

A

`I(2n)-I(n)`

B

`I(2n)-16 I(n)`

C

`I(2n)-8I(n)`

D

`I(2n)-4I(n)`

Text Solution

Verified by Experts

The correct Answer is:
B
`I(2n)=1^(4)+2^(4)+3^(4)+…+(2n-1)^(4)+(2n)^(4)`
`=[(1^(4)+3^(4)+5^(4)+..+(2n-1)^(4)]+2^(4)(1^(4)+2^(4)+3^(4)+4^(4)+…n^(4))`
`=sum_(r=1)^(n)(2r-1)^(4)+16xxI(n)`
`rArrsm_(r=1)^(n)(2r-1)^(4)=I(2n)-16I(n)`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. Consider the sequence 1,2,2,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th term...

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  2. The value of Sigma(i=1)^(n) Sigma(j=1)^(i) underset(k=1)overset(j) =22...

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  3. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

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  4. If tn denotes the nth term of the series 2+3+6+11+18+….. Then t50 is

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  5. The sum of series Sigma(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

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  6. If(1^2-t1)+(2^2-t2)+….+(n^2-tn)=(n(n^2-1))/(3) then tn is equal to

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  7. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

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  8. If Hn=1+12++1/ndot , then the value of Sn=1+3/2+5/3++(99)/(50) is H(50...

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  9. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

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  10. Let S=4/19+44/(19)^2+444/(19)^3+...oo then find the value of S

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  11. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

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  12. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

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  13. lim(nrarroo) Sigma(r=1)^(n) (r)/(1xx3xx5xx7xx9xx...xx(2r+1)) is equal ...

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  14. The greatest interger by which 1+Sigma(r=1)^(30) rxxr ! is divisible...

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  15. If Sigma(r=1)^(n) r^4=I(n), " then "Sigma(r=1)^(n) (2r -1)^4 is equal ...

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  16. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo is equal to 3 b. 6...

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  17. If x1,x2 …,x(20) are in H.P and x1,2,x(20) are in G.P then Sigma(r=1)^...

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  18. The value of Sigma(r=1)^(n) (a+r+ar)(-a)^r is equal to

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  19. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

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  20. The sum of 20 terms of the series whose rth term s given by kT(n)=(-1)...

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