Right = (- 1) 0
The original equation holds.
(2) Assuming that n=k(k∈N*, k≥ 1), the equation holds.
That is,12-22+32-42+…+(-1) k-1k2 = (-1) k-1.
Then, when n=k+ 1
12-22+32-42+…+(- 1)k- 1 k2+(- 1)k(k+ 1)2
=(- 1)k- 1
+(- 1)k (k+ 1)2
When n = k+ 1, the equation also holds.
From (1)(2), any n∈N* has.
12-22+32-42+…+(- 1)n- 1 N2 =(- 1)n- 1