The value of 2·P0   1-3·P1   2+4·P2   3-………. upto 51th  term +1!-2!+3!-…… up to 51th term  is equal to :

S=21P0-32P1+43P2+……51 tems +(1!-2!+3!-4!+……51 terms )=2.1-3.2!+4.3!+........-51(50)!+52(51)!+1!-2!+3!-4!+…....-50!+51! )=2!-3!+4!-5!+……-51!+52!+(1!-2!+3!-4!+…..+51!)=1+52!