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## Main Question or Discussion Point

Hi,

I need to prove the following:

[tex] 1+ \frac{ 1}{ 2!} + \frac{1 }{3!} +...+ \frac{ 1}{ n!} < 2 \lbrack 1 - ( \frac{ 1}{2 } )^n \rbrack [/tex]

From trying various example I'm fairly sure the relation holds but I can't seem to prove it algebraically?

Does the ineqaulity make a difference? Or can you behave pretty mcu as if it was an "=" ?

I tried simply doing 2[1-(1/2)^n] + 1/(n+1)! to try to get to 2[1-(1/2)^n+1]

but I can't seem to get very far?

Can anyone shed any light?

I need to prove the following:

[tex] 1+ \frac{ 1}{ 2!} + \frac{1 }{3!} +...+ \frac{ 1}{ n!} < 2 \lbrack 1 - ( \frac{ 1}{2 } )^n \rbrack [/tex]

From trying various example I'm fairly sure the relation holds but I can't seem to prove it algebraically?

Does the ineqaulity make a difference? Or can you behave pretty mcu as if it was an "=" ?

I tried simply doing 2[1-(1/2)^n] + 1/(n+1)! to try to get to 2[1-(1/2)^n+1]

but I can't seem to get very far?

Can anyone shed any light?

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