If f(x) = (1 + x)(1 + 2x)(1 + 3x) . . . (1 + nx), find f'(0).

Chapter 2.3: The Product Rule

11
b. If f(x) = (1 + x)(1 + 2x)(1 + 3x) . . . (1 + nx), find f'(0).

Remember that the series 1 + 2 + 3 + ... + n takes the formula n(n+1)/2.

Further reading:
-Triangular numbers
-Pascal's triangle
-Sequences and Series
-Telescoping Series

From Nelson Calculus and Vectors 12
Chapter 2.3, page 91 question 11b