How many terms are perfect square in the sequence
4,44,444,4444,44444............................
and why?
give the appropriate reason also
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1 Answers
Asish Mahapatra
·2010-03-26 01:58:43
only 1..
Let the rth term be a perfect square.
=> 11111.. r 1's will be a perfect sqare
But 11111... r times = 3 mod(4) for r≥2
for r=1, it is 1 = 0mod(4)
Now a perfect sq. is 0 or 1 mod(4)
Hence only one term is a perfect square... which is the first term i.e. 4