Question

1(1/2)+1(2/3)+1(3/4)+1(4/5)+1(5/6)+1(6/7)+1(7/8)+1(8/9)+1(9/10)+1(10/11)+1(11/12)+1(12/13)+1(13/14)+1(14/15)+1(15/16)+1(16/17)+....+1(30/31) = ??

Answer 1

Ответ:

Десятичный вид:  27.93429326

Пошаговое объяснение:

Answer 2

The expression you've provided seems to be a sum of fractions where each fraction is of the form 1(n / (n+1)) for n ranging from 1 to 30.

Let's calculate the value of this sum:

1(1/2) + 1(2/3) + ... + 1(30/31)

Notice that each term in the form 1(n / (n+1)) simplifies to just 1 - (1 / (n+1)). So, the sum can be written as:

(1 - 1/2) + (1 - 1/3) + ... + (1 - 1/31)

Now, this is equivalent to summing up a series where each term is 1 minus the reciprocal of (n+1), and n ranges from 1 to 30.

The sum of this series can be calculated as follows:

(1 - 1/2) + (1 - 1/3) + ... + (1 - 1/31) = 1 + 1 + ... + 1 - (1/2 + 1/3 + ... + 1/31)

The sum of the ones is simply 30 (since there are 30 terms).

Now, let's calculate the sum of the reciprocals:

1/2 + 1/3 + ... + 1/31

To get a common denominator, let's multiply each fraction by the least common multiple of the denominators, which is 2 * 3 * 4 * ... * 31.

(1/2) * (2/2) + (1/3) * (2/3) + ... + (1/31) * (2/31)

Now, calculate the sum of these terms:

1 + 2/3 + ... + 2/31

Next, subtract this sum from the total of 30 ones:

30 - (1 + 2/3 + ... + 2/31)

Unfortunately, this is a bit complex to compute manually. If you're looking for an approximate decimal value for this expression, you might need to use a calculator or a computational tool. If you have access to a programming language like Python, you could write a script to calculate the sum accurately.