Find the sum of the series:7/2 + 19/6 + 37/12 + ..... + 14491/4830.

1) 14559/70
2) 15449/69
3) 214
4) 212

• 7/2 + 19/6 + 37/12 + ..... + 14491/4830
  The term is
  [n (n+1)*3 +1]/n (n+1)
  So 4830 =69*70
  Clearly last term is 69th term
  Now
  Let see the sum pattern
  7/2 = 3 + ( 1/1 - 1/2)
  19/6 = 3 + (1/2 - 1/3)
  So
  3 + (1/1 - 1/2) + 3 + (1/2 - 1/3)
  3+3 + (1/1 - 1/2 + 1/2 - 1/3)
  6 + (1/1 - 1/3)
  6+ (2/3)
  20/3
  So sum format is
  3n + [ 1/1 - 1/(n+1) ]
  3n + [ n/(n+1) ]
  Sum of 69th term
  3 (69) + [ 69/70 ]
  207 + (69/70)
  207 (70) +69 / 70
  14559/70
• 8 years agoHelpfull: Yes(1) No(0)