Let S=(11⋅ 10P0−12⋅ 11P1+13⋅ 12P2−⋯−20⋅ 19P9)+( 12P2− 13P3+ 14P4−⋯+ 20P10)⋯(1) and
S1=(11⋅ 10P0−12⋅ 11P1+13⋅ 12P2−⋯−20⋅ 19P9)⋯(2)
Using: n⋅ n−1Pr−1= nPr,
Equation (2) becomes
⇒S1= 11P1− 12P2+ 13P3− 14P4+⋯− 20P10
putting the value of S1 in (1)
⇒S=( 11P1− 12P2+ 13P3− 14P4+⋯− 20P10)+( 12P2− 13P3+ 14P4−⋯+ 20P10)
⇒S= 11P1=11