Tougher than the last two

Algebra Level 5

Find the coefficient of $x^{40}$ in the expansion of the product below.

$\large{\prod _{ n=1 }^{ 50 }{ \left( x+4n \right) } }$

The length of the answer is nearly 35 digits so when you know the trick you may use a calculator and please post the solution.

1 solution

Jon Haussmann
Jan 27, 2016

Go to Wolfram Alpha and enter "4^10*S1(51,41)". Done.

This sum is related to Stirling Numbers of the First Kind , which Wolfram Alpha is capable of computing.

Wow never knew of that (+1). Can you explain from where do you know so much and how are you so good in mathematics?

Department 8 - 5 years, 4 months ago

I've just been doing this a long time. Keep practicing, and you'll know a lot too.

Jon Haussmann - 5 years, 4 months ago

sir please try this

Department 8 - 5 years, 4 months ago

Can you please post the full solution?

Sathyam Tripathi - 5 years, 4 months ago

I also used wolfram and I wanted to know how to do these type of questions.

Department 8 - 5 years, 4 months ago