If `(1+x)^n=sum_(r=0)^n C_rx^r` then prove that `C_1+2C_2+3C_3+.....+nC_n=n2^(n-1)`

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(1)+2C_(2)+3C_(3)+....+nC_(n)=n2^(n-1)

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r), then prove that C_(1)+2c_(2)+3C_(1)+...+nC_(n)=n2^(n-1)...

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(0)+2C_(1)+3C_(2)+.....+(n+1)C_(n)=2^(n-1)(n+2)

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(0)+(C_(1))/(2)+......+(C_(n))/(n+1)=2

If (1+x)^n=sum_(r=0)^nC_rx^r prove that (2^2C_0)/(1 . 2)+(2^3C_1)/(2 . 3)+....+(2^(n+2) C_n)/((n+1)(n+2))=(3^(n+2)-2n-5)/((n+1)(n+2))

If (1+x)^(n) = overset(n)underset(r=0)Sigma C_(r)x^(r ) , then prove that C_(1)+2C_(2)+3C_(3)+…..+nC_(n)=n2^(n-1) .

If (1+x)^n=sum_(r=0)^n C_rx^r then prove that sum_(r=0)^n (C_r)/((r+1)2^(r+1))=(3^(n+1)-2^(n+1))/((n+1)2^(n+1))

If (1+x)^n=underset(r=0)overset(n)C_(r)x^r then prove that C_(1)^2+2.C_(2)^(2)+3.C_(3)^2 +…….+n.C_(n)^(2)=((2n-1)!/((n-1)!)^2