Question

Prove that- 1.1P1 + 2.2P2 + 3.3P3 + .... + n.nPn = (n+1)P(n+1) - 1​

Answer 1

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Answer 2

=>1P1 + 2.2P2 + 3.3P3 + .... + n.nPn =

(n+1)P(n+1) - 1​ is true.

Step-by-step explanation:

We have,Pm=mPm=m! So, =1+1.P1+2.P2+3.P3+...+n.Pn=1+1+2.2!+3.3!=+4.4!+...+n.n!=1+∑nr=1r.r!=1+∑nr=1{(r+1)−1}=r!=1+∑nr=1[(r+1)r!−r!]=1+∑nr=1[(r+1) =−r!]=1[(2!−1!)+(3!−2!)+(4!−3!)+...+((n+1)!=−n!)]=1+((n+1)!−1!)=(n+1)!