How do you find a_10 given a_n=2^n/n! ?

Diana Suarez

Diana Suarez

Answered question

2022-09-20

How do you find a 10 given a n = 2 n n ! ?

Answer & Explanation

Ashlynn Delacruz

Ashlynn Delacruz

Beginner2022-09-21Added 9 answers

We have the general expression a n = 2 n n ! and are looking for a 10 . That gives us:
a 10 = 2 10 10 !
And now let's evaluate it! (I'll express the numbers 8 and 4 in terms of 2 x to make cancellations and simplification more obvious):
= 2 3 × 2 2 × 2 × 2 × 2 × 2 2 10 × 9 × 2 3 × 7 × 6 × 5 × 2 2 × 3 × 2
= 2 3 × 2 2 × 2 × 2 × 2 × 2 2 10 5 × 9 × 2 3 × 7 × 6 3 × 5 × 2 2 × 3 × 2
= 4 5 × 9 × 7 × 3 × 5 × 3 = 4 14 , 175

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