BdMO National 2012: Higher Secondary 04

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Moon
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BdMO National 2012: Higher Secondary 04

Problem 4:
Consider the pattern অআআইইইঈঈঈঈউউউউউ... When the part with $11$ ‘ঔ’s end, the pattern continues with $12$ ‘অ’s, $13$ ‘আ’s and so on. What is the $2012^{th}$ letter in this pattern?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

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turash
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Re: BdMO National 2012: Higher Secondary 04

etar ans asbe 8 th borno ( amar mbl e bangla lekha jay na) . ekhane borno gulo periodic vabe ase bt proti bar tar stahn er sathe 11 add hoy. .

nafistiham
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Re: BdMO National 2012: Higher Secondary 04

প্রথমে একবার অ থেকে ঔ পর্যন্ত যেতে ৬৬ টি বর্ণ লাগে এর পর প্রতিবারে ১১ করে যোগ হয় ।
অর্থাৎ, অনুক্রম টা এমনঃ
$৬৬+৭৭+৮৮+৯৯+১১০+......\approx ২০১২$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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