सिद्ध कीजिए कि `((1+x)/(1-x))^(n)=1+n((2x)/(1+x))+(n(n+1))/(1.2)((2x)/(1+x))^(2)+`....

If |x|<1 then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+......oo

If |x| lt 1 then 1+n ((2x)/(1+x))+(n(n+1))/(2!) ((2x)/(1=x))^2 + ….....oo=

If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is equal to

If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is equal to

Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...

|x|<1, then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+ is equal to a.((2x)/(1+x))^(n) b.((1+x)/(2x))^(n) c.((1-x)/(1+x))^(n) d.((1+x)/(1-x))^(n)

Prove that 1-""^(n)C_(1) (1+x)/(1+n x)+""^(n)C_(2) (1+2x)/((1+n x)^(2)) ""^(n)C_(3) (1+3x)/((1+n x)^(3)) +….(n+1) terms = 0