1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove that n.1 + (n-1).2 + (n-2).3 . 3.(n-2) + 2.(n-1) + 1.n = n(n+1)(n+2)/6 By

  1. Jul 17, 2011 #1
    Prove that n.1 + (n-1).2 + (n-2).3 ....... 3.(n-2) + 2.(n-1) + 1.n = n(n+1)(n+2)/6 By

    You cant put n=1 in the L.H.S, when we take p(1) it means the first term i.e. 'n.1' and in the R.H.S n=1 should be put that means p(1) : n.1=1 which is wrong...now can you answer it...plz solve it??
     
  2. jcsd
  3. Jul 17, 2011 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    HI Arnab! Welcome to PF! :wink:
    Yes we can …

    the LHS has n terms, so if n = 1, that's 1 term, and the LHS is 1
    .1 = 1 (and the RHS is 1.2.3/6 = 1 also). :smile:
     
  4. Jul 17, 2011 #3
    Re: Prove that n.1 + (n-1).2 + (n-2).3 ....... 3.(n-2) + 2.(n-1) + 1.n = n(n+1)(n+2)/

    Yes, by plugging in n=1, we consider the first term only on LHS and that is = 1
    Also substituting n = 1 on RHS, we get 1
    Hence, nothing wrong when n=1
     
  5. Jul 19, 2011 #4
    Re: Prove that n.1 + (n-1).2 + (n-2).3 ....... 3.(n-2) + 2.(n-1) + 1.n = n(n+1)(n+2)/

    \begin{aligned}\sum_{k=1}^{n} (n-k+1)k = (n+1)\sum_{k=1}^{n}k-\sum_{k=1}^{n}k^2= (n+1)\left[ \frac{1}{2} n (n+1)\right]-\frac{1}{6}n (n+1) (2 n+1) = \frac{1}{6}n (n+1) (n+2).\end{aligned}
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove that n.1 + (n-1).2 + (n-2).3 . 3.(n-2) + 2.(n-1) + 1.n = n(n+1)(n+2)/6 By
  1. 1+2+3+ +n= ? (Replies: 8)

  2. Is 1/(n-2) convergent? (Replies: 3)

Loading...