The sum of first n terms in a sequence is always 1/n.Find the product of the first 2014 terms (n! denotes the factorial of n,that is the product of the numbers(1,2……n))

a)-1/(2013!2013!)

b) 1/(2013!2013!)

c) 1/(2013!2014!)

d)- 1/(2013!2014!)

• we solve it by generalized example
  like we have a series like: 1 -1/2 -1/6 -1/12 we take 4 term
  so it is clear that if term is even then ans is negative
  multiply= -1/144 that means -1/ 3!*4!
  means answer d)- 1/(2013!2014!) is correct
• 8 years agoHelpfull: Yes(14) No(6)
• as per the ques sum of 1 term is 1/1=1,2 terms=1/2,3 terms=1/3 and so on. now from here we can find the 2nd term ,3rd term which are -1/2, -1/6 and so on. Now as Shashank has correctly stated the product thus becomes (-1)^n-1/n!(n-1)! so the correct answer is d.
• 8 years agoHelpfull: Yes(8) No(3)
• cannot understand plz explain....
• 8 years agoHelpfull: Yes(3) No(2)
• Sn = 1/n
  Let, Ti denote the ith term, Si denote the sum upto ith term.
  S1=T1=1/1=1.
  
  S2=1/2
  hence, T2=S2-S1=1/2 - 1 = -1/2
  
  S3=1/3
  hence, T3=S3-S2= 1/3 - 1/2 = -1/6
  
  similarly, T4= -1/12 and so on.
  
  hence, for 4 terms, product = (1) (-1/2) (-1/6) (-1/12) = (-1/144) = -1/(3! * 4!)
  
  hence by observing, option (d) -1/(2013! * 2014!) is correct.
• 6 years agoHelpfull: Yes(0) No(0)