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Question

Cho A= 3/5.2! + 3/5.3! + 3/5.4! +...+ 3/5.100!. CMR A

Answer 1

CMR A như thế nào?

Comments

Mình quên A < 0,6 nữa nhé!

Answer 2

A=3/5.2!+3/5.3!+...+3/5.100!

A=3/5(1/1.2+1/1.2.3+...+1/1.2.3.....100)

Ta có : 1/1.2=1/1.2

            1/1.2.3=1/2.3

            1/1.2.3.4<1/3.4</span>

            .........................

            1/1.2.3....100<1/99.100</span>

B=1/1.2+1/2.3+1/3.4+...+1/99.100

B=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100

=>B=1-1/100

=>B=99/100<1</span>

=>3/5B<3/5.1</span>

=>3/5(1/1.2+1/1.2.3+1/1.2.3.4+...+1/1.2.3.....100)<3/5B<3/5</span>

=>A<3/5</span>

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