A Pre-RMO question! -7

Algebra Level 1

Let a 1 = 97 a_1=97 and a n = n a n − 1 a_n=\dfrac{n}{a_{n-1}} for n > 1 n > 1 . Find a 1 a 2 a 3 a 4 a 5 a 6 a_1a_2a_3a_4a_5a_6 .


The answer is 48.

Zakir Husain by Zakir Husain , 41, India

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1 solution

a 1 a 2 a 3 a 4 a 5 a 6 = a 1 × 2 a 1 × a 3 × 4 a 3 × a 5 × 6 a 5 = a_1a_2a_3a_4a_5a_6=a_1\times \frac{2}{a_1}\times a_3\times \frac{4}{a_3}\times a_5\times \frac{6}{a_5}=

2 × 4 × 6 = 48 2\times 4\times 6=\boxed {48} .

In general, a 1 a 2 a 3 a 4 . . . a 2 n = 2 n n ! a_1a_2a_3a_4...a_{2n}=\boxed {2^nn!} .

3 Helpful 4 Interesting 3 Brilliant 1 Confused

@Alak Bhattacharya good solution

Zakir Husain - 1 year ago

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