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Sequences and Series

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  1. 501.The value of [1 + 1 1 + 2 + 1 1 + 2 + 3 + ,,....,, + ,,1 1 + 2 + 3 + ,,.....,, + ,,11] is …
  2. 502.Let be a sequence such that [a_1+a_2++a_n=n^2+3 n(n+1)(n+2)].
  3. 503.The sum [_n = 1^ 2n^2 + 3n + 4 (2n)! ] is equal to :
  4. 504.For three positive integers p, q, r, x^pq^2 = y^qr = z^p^2r and r = pq + 1 such that 3, 3 …
  5. 505.Let a, b, c>1, a^3, b^3 and c^3 be in A.P., and _a b, _c a and _b c be in G.P.
  6. 506.If [a_n = - 2 4n^2 - 16n + 15], then [a_1 + a_2, + ,...., + ,a_25] is equal to :
  7. 507.Let [S_K=(1+2++K)/(K)] and [_j=1^n S_j^2=(n)/(A)(B n^2+C n+D)], where [A, B, C, D N] and A…
  8. 508.[ The 20^ th term from the end of the progression 20,19 (1)/(4), 18 (1)/(2), 17 (3)/(4), ,…
  9. 509.If [ _e a, _e ~b, _e c] are in an A.P.
  10. 510.Let A B C be an equilateral triangle.
  11. 511.A software company sets up m number of computer systems to finish an assignment in 17 days…
  12. 512.Let a, a r, a r^2, ............
  13. 513.If the sum of the series [11 (1+d)+1(1+d)(1+2 ~d)++1(1+9 ~d)(1+10 ~d)] is equal to 5, then…
  14. 514.Let S_n=(1)/(2)+(1)/(6)+(1)/(12)+(1)/(20)+ upto n terms.
  15. 515.For positive integers n, if 4 a_n=(n^2+5 n+6) and S_n=_k=1^n((1)/(a_k)), then the value of…
  16. 516.Let T_r be the r^ th term of an A.P.
  17. 517.Let a_1, a_2, a_3, be in an A.P.
  18. 518.If the sum of the first 20 terms of the series (4 1)/(4+3 1^2+1^4)+(4 2)/(4+3 2^2+2^4)+(4 …
  19. 519.Consider two sets A and B, each containing three numbers in A.P.