#5) show: 2+5+8+...+3n-1+3n+2 = (1/2)(n+1)(3n+4)
#5)assume: 2+5+8+...+3n-1 = (1/2)n(3n+1)
#5) prove: 3n+2 = (1/2)(n+1)(3n+4) - (1/2)n(3n+1)
(1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)
((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify()
((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_trig()
((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_radical()
((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_rational()