Question Number 103796 by bemath last updated on 17/Jul/20

Σ_(k = 1) ^n k^5  = ?

Commented bymr W last updated on 17/Jul/20

Commented bybemath last updated on 17/Jul/20

waw..complete sir.  haha==.cooll

Answered by Ar Brandon last updated on 17/Jul/20

Consider;  k^6 −(k−1)^6 =k^6 −(k^6 −6k^5 +15k^4 −20k^3 +15k^2 −6k+1)                          =6k^5 −15k^4 +20k^3 −15k^2 +6k−1  ⇒Σ_(k=1) ^n [k^6 −(k−1)^6 ]=6Σ_(k=1) ^n k^5 +Σ_(k=1) ^n [−15k^4 +20k^3 −15k^2 +6k−1]  ⇒n^6 =6Σ_(k=1) ^n k^5 −15Σ_(k=1) ^n k^4 +20Σ_(k=1) ^n k^3 −15Σ_(k=1) ^n k^2 +6Σ_(k=1) ^n k−Σ_(k=1) ^n (1)  Substituting the previous series and making Σ_(k=1) ^n k^5   the subject, we get our answer.