Sequences And Series

Step 1: Simplifying the given series.
The given series is:

1%20%2B%201!%20%2B%202.2!%20%2B%203.3!%20%2B%20%5Ccdots%20%2B%20n.n!

This is equivalent to:

%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%20k%20%5Ccdot%20k!

which simplifies to:

%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%20(k%2B1)!%20-%201

Step 2: Summing the series.
The sum of the first

n

terms of the series is:

(n%2B1)!%20-%201

Step 3: Conclusion.
The value of the series is

n!%20%2B%201

. The correct answer is (2) $n!%20%2B%201$ .

Chapter Questions
1 MCQs