1+1/2^3 + 1/3^3 +1/4^3……+1/n^3
≤1+1/8 + 1/27 +1/(4*3*4)……+1/[4*(n-1)*n]
=1+1/8 + 1/27+(1/4){ 1/(3*4)……+1/[ (n-1)*n]}
=1+1/8 + 1/27+(1/4)[ 1/3-1/4+……+1/(n-1)-1/n]
=1+1/8 + 1/27+(1/4)( 1/3-1/n)
=1+1/8+1/27+1/12 -1/4n
≤1+1/8+1/24+1/12 -1/4n
=5/4 -1/4n
≤5/4