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Sequences and Series

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  1. 451.Let a1, a2, .
  2. 452.If a1, a2, a3, .....
  3. 453.For x [ ] R, let [x] denote the greatest integer [ ] x, then the sum of the series [[ - 1 …
  4. 454.Let Sn denote the sum of the first n terms of an A.P.
  5. 455.If sin4[ ] + 4 cos4[ ] + 2 = 4[ 2 ] sin [ ] cos [ ]; [ ], [ ] [ ] [0, [ ]], then cos([ ] +…
  6. 456.If nC4, nC5 and nC6 are in A.P., then n can be :
  7. 457.If the sum of the first 15 terms of the series [( 3 4 )^3 + ( 11 2 )^3 + ( 21 4 )^3 + 3^3 …
  8. 458.The sum [_k = 1^20 k1 2^k ] is equal to
  9. 459.If three distinct numbers a, b, c are in G.P.
  10. 460.The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F.
  11. 461.Some identical balls are arranged in rows to form an equilateral triangle.
  12. 462.Let the sum of the first n terms of a non-constant A.P., a1, a2, a3, .....
  13. 463.Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P.
  14. 464.If a, b, c be three distinct real numbers in G.P.
  15. 465.Let S be the sum of the first 9 terms of the series : x + ka + x2 + (k + 2) (a] + x3 + (k …
  16. 466.If the sum of first 11 terms of an A.P., a1, a2, a3, ....
  17. 467.If |x| < 1, |y| < 1 and x [ ] y, then the sum to infinity of the following series (x + y) …
  18. 468.If the sum of the series 20 + 19[3 5] + 19[1 5] + 18[4 5] + ...
  19. 469.Let a1, a2, ..., an be a given A.P.
  20. 470.If 1+(1--22.1)+(1--42.3)+(1-62.5)+......+(1-202.19)= [ ] - 220[ ], then an ordered pair [(…
  21. 471.If 210 + 29.31 + 28 .32 +.....+ 2.39 + 310 = S - 211, then S is equal to :
  22. 472.If [3^2 2 - 1], 14 and [3^4 - 2 2 ] are the first three terms of an A.P.
  23. 473.The common difference of the A.P.
  24. 474.Let a , b, c , d and p be any non zero distinct real numbers such that (a2 + b2 + c2)p2 --…
  25. 475.Five numbers are in A.P.
  26. 476.Let f : R [ ] R be such that for all x [ ] R (21+x + 21--x), f(x) and (3x + 3--x) are in A…
  27. 477.Let an be the nth term of a G.P.
  28. 478.Let S1 be the sum of first 2n terms of an arithmetic progression.
  29. 479.Let Sn = 1 .
  30. 480.Let a1, a2, ..........., a21 be an AP such that [_n = 1^20 1 a_na_n + 1 = 4 9 ].
  31. 481.Let Sn denote the sum of first n-terms of an arithmetic progression.
  32. 482.Let Sn be the sum of the first n terms of an arithmetic progression.
  33. 483.The sum of the series [1 x + 1 + 2 x^2 + 1 + 2^2 x^4 + 1 + ......
  34. 484.If the sum of an infinite GP a, ar, ar2, ar3, .......
  35. 485.The sum of the infinite series [1 + 2 3 + 7 3^2 + 12 3^3 + 17 3^4 + 22 3^5 + ......] is eq…
  36. 486.If 0 < x < 1 and [y = 1 2x^2 + 2 3x^3 + 3 4x^4 + ....], then the value of e1 + y at [x = 1…
  37. 487.If for x, y [] R, x > 0, y = log10x + log10x1/3 + log10x1/9 + ......
  38. 488.Let a1, a2, a3, .....
  39. 489.Three numbers are in an increasing geometric progression with common ratio r.
  40. 490.Let x, y > 0.
  41. 491.The sum 1 + 2 .
  42. 492.Consider two G.Ps.
  43. 493.Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 .
  44. 494.Suppose [a_1, a_2, , a_n], ..
  45. 495.Let [S = 2 + 6 7 + 12 7^2 + 20 7^3 + 30 7^4 + ,.....].
  46. 496.If a1, a2, a3 ......
  47. 497.[x = _n = 0^ a^n,y = _n = 0^ b^n,z = _n = 0^ c^n ], where a, b, c are in A.P.
  48. 498.Let A1, A2, A3, .......
  49. 499.[ aligned & Let a_n_n=0^ be a sequence such that a_0=a_1=0 and &a_n+2=3 a_n+1-2 a_n+1, n 0…
  50. 500.Let [ a_n _n = 0^ ] be a sequence such that a_0 = a_1 = 0 and a_n + 2 = 2a_n + 1 - a_n + 1…