Series

Página 1

nΣ1 r = 1/2n(n+1)

nΣ1 r^2 = 1/6n(n+1)(2n+1)

nΣ1 r^3 = 1/4n^2(n+1)^2

nΣ1 (2r^3 + r) = nΣ12r^3 + nΣ1 r = 2(0.25(n)^2(n+1)^2) + 0.5(n)(n+1)

=> 0.5(n^2)(n+1)^2 + 0.5(n)(n+1)

=> (n+1)^2 = (n+1)(n+1) = n^2 + 2n + 1

=> 0.5(n^2 + 2n + 1)(n^2) + 0.5(n)(n+1)

=> 0.5(n^4 + 2n^3 + n^2) + 0.5(n^2 + n)

=> (n^4/2 + n^3 + n^2/2) + (n^2/2 + n/2)

=> n^4/2 + n^3 + n^2 + n/2