please solve this question

In Problems 5-10, determine whether the given sequence converges or diverges. 5. 3ni + 2 n+ ni 6. J ni + 2" 3ni + 5" 7 . (ni + 2)21 n'i 8. n(1+ i") n +1 9 . {ntin n 10. elin + 2 (tan 'n)i In Problems 11 and 12, show that the given sequence {{ } converges to a complex number L by computing limn- Re(an) and limn-+. Im(2n) 11. J An + 3ni 2n + i 12 . In Problems 13 and 14, use the sequence of partial sums to show that the given series is convergent. 13. E 1 Ki k + 2i k+ 1+2i 14. 2 k ( k + 1 ) In Problems 15-20, determine whether the given geometric series is convergent or divergent. If convergent, find its sum. 15. 16. 17. K= 1 18. 19. 1 + 2i 20. (1 +i)k-1 In Problems 21-30, find the circle and radius of convergence of the given power series. 21. E 1 Ko ( 1 - 21) k+1 ( 2 - 21 ) k 22. 23. 2 (-1)k kel k2k ( 2 - 1 - 2)k 24. K1 k2 (3 + 4i) k ( 2 + 32)k 25. E (1 + 32)*(2 - 1)k 26. 2k 27. (2 -4- 32)k 52k 28. (-1)k (1 + 2i )k 2 ( 2 + 2i ) k 29 (2k)! Ko (k + 2) (k!)2 ( 2 - 2)2k k! 30. 10 (21) KZ 23k