- #1
Bazman
- 21
- 0
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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