In: Advanced Math

Prove by induction:

1 + 1/4 + 1/9 +⋯+ 1/?^2 < 2 − 1/?,

for all integers ?>1

We will use induction on to prove that , for .

**Base Step :** For
,

As ,

So the statement is true for .

**Induction Hypothesis :** Suppose the statement is
true for
that is ,

**Induction Step :** For
,

, Using induction Hypothesis .

, as .

So , .

That is the statement is true for if we assume it is true for . Also the statement is true for . Hence by induction on the statement is true for all or for all .

Hence , for .

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If you have doubt or need more clarification at any step please comment .

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