# in the expansion (1+x) (1+x+x^2) ... (1+ x + x^2 +...+ x^2n) the sum of the coefficients is ?

SUm of the coefficient of any expression is obtained by putting the variable=1 in the expression.

So if we put x=1 in the expression

$(1+x)(1+x+{x}^{2})..(1+x+{x}^{2}+....{x}^{2n}),\phantom{\rule{0ex}{0ex}}weget(1+1)(1+1+1)...(1+1+1...1(2n+1times\left)\right)\phantom{\rule{0ex}{0ex}}=2.3.4......(2n+1)=1.2.3.4......(2n+1)=(2n+1)!\phantom{\rule{0ex}{0ex}}$

Hope you are clear with this

With regards

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