Question

你能化简﹙x－1﹚﹙x∧99＋x∧98＋x∧97···＋x＋1﹚吗?我已经求出了x∧100－1

Answer 1

1+x+x^2+...+x^99 = (x^100 -1)/(x-1)

(x-1)(1+x+x^2+...+x^99) = x^100 -1

﹙﹣2﹚∧50＋﹙﹣2﹚∧49＋···＋﹙﹣2﹚＋1

=[1- (-2)^51]/(1+2)

=(1/3)[ 1-(-2)^51]