Question

1:6*7+1:7*8+1:8*9+...+1:21*22А)4/33Б)5/22В)3/11Г)7/3

Answer 1

Ты че ту просто делить, умножать и складывать не умеешь?

Answer 2

To solve the given expression, let's break it down step by step:

1/6 * 7 + 1/7 * 8 + 1/8 * 9 + ... + 1/21 * 22

To simplify the expression, we can start by finding a common denominator for all the fractions involved. In this case, the least common multiple (LCM) of the denominators from 6 to 21 is 27720.

Now, we can rewrite the expression with the common denominator:

(1/6) * (7 * 27720/6) + (1/7) * (8 * 27720/7) + (1/8) * (9 * 27720/8) + ... + (1/21) * (22 * 27720/21)

Simplifying further, we have:

(1/6) * (7 * 4620) + (1/7) * (8 * 3960) + (1/8) * (9 * 3465) + ... + (1/21) * (22 * 1320)

Now, we can simplify each term and add them together:

(7 * 4620)/(6 * 6) + (8 * 3960)/(7 * 6) + (9 * 3465)/(8 * 6) + ... + (22 * 1320)/(21 * 6)

Calculating each term:

(32340 + 28560 + 31275 + ... + 31920)/(6 * 6)

To find the sum of the terms in the numerator, we can factor out 2640:

2640 * (1 + 2 + 3 + ... + 12)

The sum of the first n positive integers can be found using the formula n(n + 1)/2. In this case, n = 12:

2640 * (12 * 13)/2

2640 * 78

205920

Now, we can substitute this value back into the expression:

205920/(6 * 6)

205920/36

5720

Therefore, the value of the given expression is 5720.

None of the provided options (A) 4/33, (B) 5/22, (C) 3/11, or (D) 7/3 correspond to the calculated value. Please double-check the expression and options provided.