Question

1/(25*26) + 1/(26*27) + ... + 1/(49*50)

Answer 1

Ответ:

Пошаговое объяснение:

1/(25*26) + 1/(26*27) + ... + 1/(49*50)= 1/50=0,02

50-25=25- число действий

25-1=24 -число промежутков (к каждому промежутку +2)

24*2=48 - добавленное число

49*50=2450

2450:25-48=50 - ЗНАМЕНАТЕЛЬ

1 - числитель

1/50=0,02

Answer 2

The expression you've given is a sum of fractions where each fraction has a numerator of 1 and a denominator that is the product of two consecutive integers. To simplify this sum, you can use the following formula for the sum of a series of fractions with consecutive integer denominators:

1/n(n+1) = 1/n - 1/(n+1)

You can apply this formula to each fraction in the series, and then simplify the resulting expression. Here's the step-by-step calculation:

1/(2526) + 1/(2627) + ... + 1/(49*50)

= (1/25 - 1/26) + (1/26 - 1/27) + ... + (1/49 - 1/50)

Notice that the -1/26 and 1/26 in the first and second terms, respectively, cancel each other out, and this pattern continues for all the terms in the series except for the first and last terms.

So, the simplified expression is:

1/25 - 1/50

Now, find a common denominator for these two fractions, which is 50:

(2/50) - (1/50) = 1/50

So, the sum of the given series is equal to 1/50.