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aartemm
@aartemm
July 2022
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Как вывести формулу суммы геометрической прогрессии?
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Yutq
Запишем сумму прогрессии в общем виде
Sn = b1 + b1q + b1q^2 + ... + b1q^(n-1)
Прибавим к сумме b1*q^n
Sn + b1*q^n = b1 + ( b1 + b1q + b1q^2 + ... + b1q^(n-1))*q = b1 + Sn*q
Sn + b1*q^n = b1 + Sn*q
Sn - Sn*q = b1 - b1*q^n
Sn*( 1-q) = b1*( 1 - q^n )
Sn = (b1*( 1 - q^n )) / (1 - q)
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Answers & Comments
Sn = b1 + b1q + b1q^2 + ... + b1q^(n-1)
Прибавим к сумме b1*q^n
Sn + b1*q^n = b1 + ( b1 + b1q + b1q^2 + ... + b1q^(n-1))*q = b1 + Sn*q
Sn + b1*q^n = b1 + Sn*q
Sn - Sn*q = b1 - b1*q^n
Sn*( 1-q) = b1*( 1 - q^n )
Sn = (b1*( 1 - q^n )) / (1 - q)