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Prove that 1+i^2+i^4+i^6 =0...

Prove that `1+i^2+i^4+i^6` =0

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum of all even integers between 101 and 199.

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  2. Match the statements/expressions given in column I with the values g...

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  3. Prove that 1+i^2+i^4+i^6 =0

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  4. if a ,b ,c are in G.P.,then (log)a 10 ,(log)b10,(log)c 10 are in

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  5. The 15th term of the series 2 1/2+1 7/(13)+1 1/9+(20)/(23)+.... i s (...

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  6. Let a1,a2,a3,.......a11 be real number satisfying a1=15,27-2a2gt0 anda...

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  7. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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

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  9. Find the conjugate of the following: sqrt (-3)

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  10. The x=1111....1 of 91 times of is a (a) Even number. (b) Prime numbe...

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

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

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

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

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

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

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

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  18. 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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  19. 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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  20. Find the sum of odd intergers from 1 to 201.

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