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(n-1)*2+(n-2)*3+(n-3)*4+

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Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+....(n−1).2+n.1"

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+....(n−1).2+n.1" also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n*1 also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+,*1 also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

If f(n)=|(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!), ((n+2)!, (n+3)!, (n+4)!)| Then the value of 1/1020[(f(100))/(f(99))] is

If f(n)=|(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!), ((n+2)!, (n+3)!, (n+4)!)| Then the value of 1/1020[(f(100))/(f(99))] is

For a fixed positive integer n if D= |(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!),((n+2)!, (n+3)!, (n+4)!)| = the show that D/((n!)^3)-4 is divisible by n.

Prove the following by using the principle of mathematical induction for all n in N :- 1.2.3 + 2.3.4 +...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 .

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .