Exercise 1537Combinatorics › Binomial coefficientsL1Added 3 Nov 2026

Generating function of binomial row

#generating function#binomial row#polynomial

Statement

Show that $\sum_{k=0}^{n}\binom{n}{k}x^k=(1+x)^n$ .

Hint

Binomial theorem.

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Binomial theorem. $(1+x)^n=\sum_k\binom{n}{k}x^k$ .

Interpretation. The row of Pascal's triangle gives the coefficients of the polynomial $(1+x)^n$ .

Conclusion. The generating function of the $n$ -th row is $(1+x)^n$ .