Question

1/10*11+1/11*12+1/12*13+...+1/19*20

Answer 1

Ответ:

0,05

Пошаговое объяснение:

1/(10*11) +1/(11*12) =...= 2/(10*12)

2/(10*12)+1/(12*13) =...= 3/(10*13)

3/(10*13)+1/(13*14) =...= 4/(10*14)

...

а/( 10*(10+а) ) +1/((10+а) *(10+а+1))=...= ( а+1)/( 10*(10+а+1))

...

9/(10*19) +1/(19*20)=...= 10/(10*20)=1/20=0,05

Answer 2

The expression you've provided seems to be a sum of terms where each term follows the pattern of adding 1 to the denominator and multiplying it with the next integer. The expression can be written as follows:

1/10 * 11 + 1/11 * 12 + 1/12 * 13 + ... + 1/19 * 20

Let's calculate this step by step:

1/10 * 11 = 11/10 1/11 * 12 = 12/11 1/12 * 13 = 13/12 ...

Continuing this pattern up to 1/19 * 20:

1/19 * 20 = 20/19

Now let's sum up all these fractions:

11/10 + 12/11 + 13/12 + ... + 20/19

Calculating the decimal values of these fractions and summing them up:

≈ 1.1 + 1.090909 + 1.083333 + ... + 1.052632

Adding all these values together will give you the final result of the expression. Please note that this sum doesn't have a simple closed-form expression, so you would need to calculate each term's decimal value and then sum them up numerically.