Question

(1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132) * 120

Answer 1

(1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132) * 120 = 20

для натурального n верно 1/n(n+1) = (n+1-n)/n(n+1) = 1/n - 1/(n+1)

1/20 = 1/(4*5) ..... 1/132 = 1/(11*12)

(1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132) * 120 = (1/4*5 + 1/5*6 + 1/6*7 + 1/7*8 + 1/8*9 + 1/9*10 + 1/10*11 + 1/11*12) * 120 = (1/4 -1/5 + 1/5-1/6 + 1/6-1/7 + 1/7-1/8 + 1/8-1/9 + 1/9-1/10 + 1/10-1/11 + 1/11-1/12) * 120 = (1/4 - 1/12) * 120 = (3/12 - 1/12) * 120 =  2/12*120 = 2*10 = 20

не надо привожить к страшным знаменателям

все легче

надо применять математическте формулы

Answer 2

(1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132) * 120 = 20

1) 1/20+1/30 =5/60 = 1/12

2) 1/42+1/56 = 1/24

3) 1/72+1/90 = 1/40

4) 1/110+1/132 = 1/60

5) 1/40 + 1/60 = 1/24

6) 1/24 + 1/24 = 1/12

7) 1/12 + 1/12 = 1/6

8) 1/6*120 = 20

Answer 3

To calculate the expression:

(1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132) * 120

You can follow these steps:

1. Calculate the sum of the fractions inside the parentheses:

   1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132

2. Find a common denominator for all these fractions, which is the least common multiple (LCM) of the denominators. The LCM of 20, 30, 42, 56, 72, 90, 110, and 132 is 1,386,720.

3. Rewrite each fraction with the common denominator:

   (1/20) * (69,336/69,336) + (1/30) * (46,224/46,224) + (1/42) * (32,928/32,928) + (1/56) * (24,812/24,812) + (1/72) * (19,260/19,260) + (1/90) * (15,408/15,408) + (1/110) * (12,570/12,570) + (1/132) * (10,488/10,488)

4. Now, you have a common denominator, and you can add the fractions:

   (69,336 + 46,224 + 32,928 + 24,812 + 19,260 + 15,408 + 12,570 + 10,488) / 1,386,720

5. Calculate the numerator:

   240,026 / 1,386,720

6. Finally, multiply the result by 120:

   (240,026 / 1,386,720) * 120

Now, you can calculate this expression:

(240,026 / 1,386,720) * 120 ≈ 20.79 (rounded to two decimal places)

So, the result is approximately 20.79.