Tired of Sequences. This one is Nice

Number Theory Level 2

Let a 0 , a 1 , a 2 , … a_{0},a_{1},a_{2},\ldots be a sequence such that a 0 = 1 a_{0}=1 and a n + 1 = ( n + 1 ) a n a_{n+1}=(n+1)a_{n} , for integer n > 0 n>0 . Which element of this sequence is equal to 123 ! 123! ?

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .

a 321 a_{321} a 231 a_{231} there is no such element a 123 a_{123}

Hana Wehbi by Hana Wehbi , 51, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Hana Wehbi
May 16, 2016

For this sequence a n = n ! a_{n}=n! . We can prove this by mathematical induction; therefore, the answer is a 123 a_{123} .

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sam Bealing
May 16, 2016

a n = n ! a_n=n! a 123 = 123 ! a_{123}=123!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...