Answer:
The smallest number of servers required is 3 servers
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Explanation:
Given


Required
Minimum number of servers needed
Let p represent the probability that a server is reliable and the probability that it wont be reliable be represented with q
Such that

It should be noted that probabilities always add up to 1;
So,
'
Subtract p from both sides


Substitute 

Convert % to fraction

Convert fraction to decimal


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<em>To get an expression for one server</em>
The probabilities of 1 servers having 99.98% reliability is as follows;

Recall that probabilities always add up to 1;
So,
Subtract q from both sides


So,


Let the number of servers be represented with n
The above expression becomes

Convert percent to fraction

Convert fraction to decimal

Add
to both sides


Subtract 0.9998 from both sides



Recall that 
So, the expression becomes

Take Log of both sides

From laws of logarithm 
So,
becomes

Divide both sides by 





<em>Hence, the smallest number of servers required is 3 servers</em>