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арифметическим прогрессиям

Noun
dative form-of plural

арифмети́ческая прогре́ссия (arifmetíčeskaja progréssija, arifmetíčeskaja progrɛ́ssija) の複数与格

English Meaning
dative plural of арифмети́ческая прогре́ссия (arifmetíčeskaja progréssija, arifmetíčeskaja progrɛ́ssija)
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数学者は等差数列に公式を適用して、数列の和を計算します.

The mathematician applies formulas to arithmetic progressions to calculate the sum of a sequence.

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арифметическими прогрессиями

Noun
form-of instrumental plural

instrumental plural of арифмети́ческая прогре́ссия (arifmetíčeskaja progréssija, arifmetíčeskaja progrɛ́ssija).

English Meaning
instrumental plural of арифмети́ческая прогре́ссия (arifmetíčeskaja progréssija, arifmetíčeskaja progrɛ́ssija)
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講義の最中に、教授は複雑な数列を等差数列と比較しました.

During the lecture, the professor compared complex numerical sequences with arithmetic progressions.

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