limx→∞23-1323+1333-1333+13…·n3-1n3+1 equals

limn→∞ ∏n=2nn3-1n3+1  =   limn→∞ ∏n=2n n-1 n2+n+1n+1 n2 -n+1  =limn→∞ ∏n=2nn-1n+1∏n=2nn2+n+1n2-n+1== limn→∞1·2·3·4·····n-13·4·5·6·········n-1·n.n+1 ×7·13·21··········n2+n+13·7·13············n2-n+1  =limn→∞2nn+1×n2+n+13 =limn→∞  21+1n+1n231+1n =23