Question

Найдите сумму бесконечно убывающей прогрессии -16; -8; -4;.....​

Answer 1

Ответ:

31.(9)

Объяснение:

-16+(-8)+(-4)-...=31.(9), то есть стремится к 32, например как гипербола не достигает нуля.

Или по формуле: S=b¹(qⁿ-1)/(q-1)

b¹=-16

q=0.5

n возьмем например 10

S=-16(0.5¹°-1)/(-0.5)=-16(-0.(9))/-0.5=-16x1.(9)=-31.(9)

С увеличением степени сумма будет приближаться к 32

Answer 2

Calculating the Sum of an Infinite Decreasing Progression

To find the sum of an infinitely decreasing progression such as -16, -8, -4, ..., we can use the formula for the sum of an infinite geometric series.

The formula for the sum of an infinite geometric series is given by:

Sum = a / (1 - r)

Where: - a is the first term of the series - r is the common ratio

In this case, the first term a is -16 and the common ratio r is 1/2 because each term is half of the previous one.

So, the sum of the infinite decreasing progression -16, -8, -4, ... is:

Sum = -16 / (1 - 1/2)

Now, let's calculate the sum.

Sum = -16 / (1/2)

Sum = -16 * 2

Sum = -32

Therefore, the sum of the infinite decreasing progression -16, -8, -4, ... is -32.

[[SOURCE #2]]