Question

1/2 умножить на 2/3 умножить на 3/4 умножить на ... равно 999/1000

Answer 1

1/2*2/3*3/4= 4

999/1000:4= 999/1000*1/4= 999/4000

1/2*2/3*3/4*999/4000= 999/1000

Answer 2

To find the value of the expression 1/2 * 2/3 * 3/4 * ..., which continues indefinitely and equals 999/1000, we can use the concept of infinite geometric progression.

Let's denote the expression as S:

S = 1/2 * 2/3 * 3/4 * ...

Notice that each term in the expression can be represented as a fraction of the form (n / n + 1), where n starts from 1 and keeps increasing by 1 for each subsequent term.

So, S can be written as:

S = (1/2) * (2/3) * (3/4) * ... * (n / n + 1)

Now, we want to find the value of S when n approaches infinity, which will be equal to 999/1000.

Let's set up the equation:

S = (1/2) * (2/3) * (3/4) * ... * (n / n + 1) = 999/1000

Since the expression continues indefinitely, we can write S as a product of two infinite series:

S = (1/2) * (2/3) * (3/4) * ... * (n / n + 1) = (1/2) * (2/3) * (3/4) * ... * (n / n + 1) * [(n + 1) / (n + 1)]

Now, notice that each term in the parentheses of the second product cancels with the term in the numerator of the next fraction:

S = (1/2) * (2/3) * (3/4) * ... * (n / n + 1) * [(n + 1) / (n + 1)] = (1/2) * (1)

Simplifying further:

S = 1/2

Thus, the infinite product 1/2 * 2/3 * 3/4 * ... is equal to 1/2 and not 999/1000 as given. There might be an error or misunderstanding in the original statement of the problem.