theorem :: SERIES_2:2

for n being Real holds
( (n + 1) |^ 3 = (((n |^ 3) + (3 * (n |^ 2))) + (3 * n)) + 1 & (n + 1) |^ 4 = ((((n |^ 4) + (4 * (n |^ 3))) + (6 * (n |^ 2))) + (4 * n)) + 1 & (n + 1) |^ 5 = (((((n |^ 5) + (5 * (n |^ 4))) + (10 * (n |^ 3))) + (10 * (n |^ 2))) + (5 * n)) + 1 ) by Lm4, Lm6;