Question

1/2+3/8+9/32+... вычислите​

Answer 1

Ответ: S=2.

Пошаговое объяснение:

(1/2)+(3/8)+(9/32); ...

b₁=1/2=0,5.

q=(3/8):(1/2)=(3/8)*(2/1)=3/4=0,75.

S=b₁/(1-q)=0,5/(1-0,75)=0,5/0,25=2.

Answer 2

(1/2)+(3/8)+(9/32);

b₁=1/2=0,5.

q=(3/8):(1/2)=(3/8)*(2/1)=3/4=0,75.

S=b₁/(1-q)=0,5/(1-0,75)=0,5/0,25=2.

Answer 3

To calculate the sum of the given infinite series, we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

where "a" is the first term of the series and "r" is the common ratio between consecutive terms.

In this case, the first term (a) is 1/2, and the common ratio (r) is 3/8. So, the sum of the infinite series is:

Sum = (1/2) / (1 - 3/8)

Now, let's perform the calculations:

Sum = (1/2) / (1 - 3/8) Sum = (1/2) / (5/8) Sum = (1/2) * (8/5) Sum = 4/5

So, the sum of the infinite series 1/2 + 3/8 + 9/32 + ... is 4/5 or 0.8.