P=R(1-(1+1)^-n/1) eching

$$P = R ( \frac { 1 - ( 1 + 1 ) ^ { - n } } { 1 } )$$

R uchun yechish

$$\left\{\begin{matrix}R=-\frac{P\times 2^{n}}{1-2^{n}}\text{, }&n\neq 0\\R\in \mathrm{R}\text{, }&P=0\text{ and }n=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 olish uchun 1 va 1'ni qo'shing.

$$P=R\times \frac{1-2^{-n}}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$P=R\left(1-2^{-n}\right)$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$R\left(1-2^{-n}\right)=P$$

R ga 1-2^{-n} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$R-R\times 2^{-n}=P$$

R'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1-2^{-n}\right)R=P$$

Tenglama standart shaklda.

$$\left(-\frac{1}{2^{n}}+1\right)R=P$$

Ikki tarafini 1-2^{-n} ga bo‘ling.

$$\frac{\left(-\frac{1}{2^{n}}+1\right)R}{-\frac{1}{2^{n}}+1}=\frac{P}{-\frac{1}{2^{n}}+1}$$

1-2^{-n} ga bo'lish 1-2^{-n} ga ko'paytirishni bekor qiladi.

$$R=\frac{P}{-\frac{1}{2^{n}}+1}$$

P ni 1-2^{-n} ga bo'lish.

$$R=\frac{P\times 2^{n}}{2^{n}-1}$$

P uchun yechish

$$P=-\frac{R}{2^{n}}+R$$