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Homework Statement
i=1 Sigma n (1/i2) <= 2 - (1/n)
The Attempt at a Solution
I've done the basic step and assumption step...little stuck on the inductive step
So far I have...
show 1 + 1/4 + 1/9 + 1/16 +...+ (1/k2) + (1/(k+1)2) <= 2 - (1/k+1)
To clarify matters:Homework Statement
i=1 Sigma n (1/i2) <= 2 - (1/n)
The Attempt at a Solution
I've done the basic step and assumption step...little stuck on the inductive step
So far I have...
show 1 + 1/4 + 1/9 + 1/16 +...+ (1/k2) + (1/(k+1)2) <= 2 - (1/k+1)
To clarify matters:
I take it that you need to prove (by induction) that:[itex]\displaystyle
\sum_{i=1}^{n}\frac{1}{i^2}\le2-\frac{1}{n}\ .[/itex]
Is that correct?
So, you have assumed that 1 + 1/4 + 1/9 + 1/16 +...+ (1/k^{2}) ≤ 2 - (1/k) ,
and you need to show that 1 + 1/4 + 1/9 + 1/16 +...+ (1/k^{2}) + (1/(k+1)^{2}) ≤ 2 - (1/(k+1)) .
Is that correct?
What have you tried, in this effort?
BTW: Please learn to use parentheses, so that your mathematical expressions say what you mean for them to say.
Let's see:Yes, that is correct...I've done equality inductive proofs, but have not encountered less than or greater than type proofs...so I'm not sure how to begin.