nC0−12nC1+13nC2−…+(−1)n nCnn+1 is equal to

We know, (1−x)n=nC0−nC1x+nC2x2…(−1)nnCnxn On integrating limit 0 to 1, we get∫01 (1−x)ndx=∫01  nC0−nC1x+nC2x2…(−1)nnCnxndx →−(1−x)n+1n+101= nC0x− nC1x22+ nC2x33…(−1)nnCnxn−1n+101⇒0+1n+1=nC0− nC12+ nC23−…(−1)n nCnn+1