Question

1.

a) Cho A = \(1+3+3^2+3^3+3^4+...+3^{2012}\)

và B = \(3^{2012}:2\)

Tính B - A

b) Tìm hai số nguyên tố x và y sao cho :

\(x^2-6y^2=1\)

c) Cho B = \(\left(1.2.3....2012\right).\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}\right)\)

CMR: B chia hết cho 2013

Answer 1

c) Cho B = (1.2.3....2012) . ( 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{2012}\) ) Chứng minh B chia hết cho 2013

B = (1.2.3....2012) . (1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + ...+ \(\dfrac{1}{2012}\) )

=(1.2.3...671...2012) . (1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{2012}\))

=(1.2.(3.671)...2012) . (1 + \(\dfrac{1}{2}\) +\(\dfrac{1}{3}\) + ... + \(\dfrac{1}{2012}\))

=(1.2.2013...2012) . (1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{2012}\))

Vậy B chia hết cho 2013

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