in the expansion (1+x) (1+x+x^2) (1+ x + x^2 + + x^2n) the sum - Maths - Binomial Theorem

Question

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

Vivek Rai · Accepted Answer

Dear student
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+x2) (1+x+x2+ x2n), we get (1+1)(1+1+1)
(1+1+1 1(2n+1times))=2 3 4 (2n+1)=1 2 3 4 (2n+1)= (2n+1)!
Hope you are clear with this
With regards

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