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Statement 1: Sum of the series 1^3-2^3+3...

Statement 1: Sum of the series `1^3-2^3+3^3-4^3++11^3=378.` - Statement 2: For any odd integer `ngeq1,n^3-(n-1)^3++(-1)^(n-1)1^3=1/4(2n-1)(n+1)^2dot`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. The x=1111....1 of 91 times of is a (a) Even number. (b) Prime numbe...

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  2. Which term of the AP 64, 60, 56, 52, 48 ,.... is 0 .

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  3. Statement 1: Sum of the series 1^3-2^3+3^3-4^3++11^3=378. - Statement ...

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  4. Statement 1: 1^(99)+2^(99)++100^(99) is divisible by 10100. Statement...

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  5. Find the nth term of the AP 8, 3, -2, -7, -12,....

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  6. The sum of three consecutiveterms of an AP is 21, and the sum of the s...

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  7. Let a1 , a2 , a3,.... be terms of an A.P. if (a1 + a2 +....+ ap)/(a1 +...

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  8. Consider an A.P. a1, a2, a3,......... such that a3+a5+a8=11 and a4+a2...

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

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  10. If |a|<1a n d|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^2)b^2+(...

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  11. Find the sum of odd intergers from 1 to 201.

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  12. If a1, a2, a3(a1>0) are three successive terms of a G.P. with common r...

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  13. Three numbers form an increasing G.P. If the middle number is doubled,...

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  14. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  15. If S1,S2 and S3 be respectively the sum of n, 2n and 3n terms of a G.P...

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  16. There are 4n + 1 terms in a sequence of which first 2n + 1 are in Arit...

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  17. If (p+q)t h term of a G.P. is a and its (p-q)t h term is b where a ,b ...

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  18. Find the sum of n terms of the series whose nth term is T(n)=tanx/(2^n...

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  19. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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  20. The first trem of a GP is -3 and the square of the second term is equa...

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