Calculate the sequence, - 1, - 1 + 3, - 1 + 3-5, - 1 + 3-5 + 7 respectively From this, we can guess that: an=-1+3-5+… +The result of (- 1) ^ n (2n-1) is proved by mathematical induction

Calculate the sequence, - 1, - 1 + 3, - 1 + 3-5, - 1 + 3-5 + 7 respectively From this, we can guess that: an=-1+3-5+… +The result of (- 1) ^ n (2n-1) is proved by mathematical induction

When n = 1, left = - 1, right = - 1. When n = k, suppose - 1 + 3-5 + +(- 1) ^ k (2k-1) = - 1) ^ k * k holds when n = K + 1, - 1 + 3-5 + +(- 1) ^ k (2k-1) + (- 1) ^ (K + 1) (2k + 1) = (- 1) ^ k * k + (- 1) ^ (K + 1) (2k + 1) = (- 1) ^ k * k - (- 1) ^ k * (2k + 1) = (- 1) ^ k (k-2k-1) = (- 1) ^ (K + 1) (K + 1) equation also holds - 1 + 3-5 + +(-1)^n(2n-1)=(-1)^n*n a1=-1 a2=-1+3=2 a3=-1+3-5=-3 a4=-1+3-5+7=4