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Sequences and Series

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  1. 401.If x=_n=0^a^n, y=_n=0^b^n, z=_n=0^c^n where a,b,c are in A.P.
  2. 402.The sum of the series 1+142!+1164!+1646!+ ad infinitum is:
  3. 403.Let T_r be the r-th term of an A.P.
  4. 404.Let two numbers have arithmetic mean 9 and geometric mean 4.
  5. 405.The sum of the series 12!+14!+16!+ is:
  6. 406.The sum of the first n terms of the series 1^2+22^2+3^2+24^2+5^2+26^2+ is n(n+1)^22 when n…
  7. 407.If S_n=_r=0^n1nr and t_n=_r=0^nrnr, then t_nS_n is equal to:
  8. 408.If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal to the sum of the s…
  9. 409.The sum of the series 112-123+134- up to is equal to:
  10. 410.If 1, _9(3^1-x+2), _3(43^x-1) are in A.P., then x equals:
  11. 411.Sum of infinite number of terms of a G.P.
  12. 412.The fifth term of a G.P.
  13. 413.1^3-2^3+3^3-4^3++9^3=
  14. 414.The value of 2^1/44^1/88^1/16 is:
  15. 415.The value of 1^3-2^3+3^3-4^3+-14^3+15^3 is:
  16. 416.The sum of the first ten terms of an A.P.
  17. 417.(13+47)+(13^2+1347+4^27^2)+(13^3+13^247+134^27^2+4^37^3)+ up to infinite terms, is equal t…
  18. 418.Sum of infinite number of terms of GP is 20 and sum of their square is 100.
  19. 419.Fifth term of a GP is 2, then the product of its 9 terms is
  20. 420.The sum of the serier [1 1.2 - 1 2.3 + 1 3.4..............] up to [ ] is equal to
  21. 421.Let T_r be the rth term of an A.P.
  22. 422.The sum of the series [1 + 1 4.2! + 1 16.4! + 1 64.6! + .......] ad inf.
  23. 423.If a_1,a_2,....a_n are in H.P., then the expression [a_1,a_2 + ,a_2,a_3, + ....
  24. 424.Let a_1, a_2, a_3.....be terms on A.P.
  25. 425.In a geometric progression consisting of positive terms, each term equals the sum of the n…
  26. 426.The sum to infinite term of the series [1 + 2 3 + 6 3^2 + 10 3^3 + 14 3^4 + .....] is
  27. 427.If [(10)^9 + 2(11)^1,(10^8) + 3(11)^2,(10)^7 + .........
  28. 428.The sum of first 9 terms of the series.
  29. 429.If the [2^nd,5^th,and,9^th] terms of a non-constant A.P.
  30. 430.If the sum of the first ten terms of the series [( 13 5 )^2 + ( 22 5 )^2 + ( 31 5 )^2 + 4^…
  31. 431.Let a1, a2, a3, .
  32. 432.Let z = 1 + ai be a complex number, a > 0, such that z3 is a real number.
  33. 433.Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3.
  34. 434.For any three positive real numbers a, b and c, 9(25a^2 + b2) + 25(c2 - 3ac) = 15b(3a + c)…
  35. 435.If three positive numbers a, b and c are in A.P.
  36. 436.Let Sn = [1 1^3] + 1 + 2 1^3 + 2^3 + 1 + 2 + 3 1^3 + 2^3 + 3^3 + .........
  37. 437.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the serie…
  38. 438.Let An = [( 3 4 ) - ( 3 4 )^2 + ( 3 4 )^3] -.
  39. 439.If a, b, c are in A.P.
  40. 440.If b is the first term of an infinite G.P.
  41. 441.If x1, x2, .
  42. 442.The sum of the first 20 terms of the series [1 + 3 2 + 7 4 + 15 8 + 31 16 + ...,] is :
  43. 443.Let [1 x_1,1 x_2,...,1 x_n,,] (xi [ ] 0 for i = 1, 2, ..., n) be in A.P.
  44. 444.Let a, b and c be in G.P.
  45. 445.Let a1, a2, a3,......be an A.P.
  46. 446.The sum [1 + 1^3 + 2^3 1 + 2 + 1^3 + 2^3 + 3^3 1 + 2 + 3 + ......
  47. 447.The sum [3 1^3 1^3 + 5 (1^3 + 2^3) 1^2 + 2^2 + 7 ( 1^3 + 2^3 + 3^3 ) 1^2 + 2^2 + 3^2 + ...…
  48. 448.If a1, a2, a3, ...............
  49. 449.If 19th term of a non-zero A.P.
  50. 450.Let x, y be positive real numbers and m, n positive integers.