Question

2/1×3+2/3×5+2/5×7+.....+2/31×33+2/33×35=?​

Answer 1

Ответ:

ну наверно этот ответ 3,253,3

Answer 2

To find the sum of the series:

2/1×3 + 2/3×5 + 2/5×7 + ... + 2/31×33 + 2/33×35

We can first simplify each term by factoring out the common factor of 2 and then calculate each term separately.

2/1×3 = 2/3 2/3×5 = 2/15 2/5×7 = 2/35

You can see a pattern forming here. Each term has the form 2/(n×(n+2)), where n is an odd number starting from 1 and increasing by 2 each time.

Now, we need to calculate each term and then add them up:

2/3 + 2/15 + 2/35 + ... + 2/(31×33) + 2/(33×35)

Let's calculate the common denominator first, which is the least common multiple (LCM) of the denominators:

LCM(3, 15, 35, ..., 33, 35) = 1155

Now, we need to express each fraction with a denominator of 1155:

(2/3) × (385/385) = 770/1155 (2/15) × (77/77) = 154/1155 (2/35) × (33/33) = 66/1155

Now, we have:

(770/1155) + (154/1155) + (66/1155) + ... + (2/(31×33)) × (1155/1155) + (2/(33×35)) × (1155/1155)

Now, we can add these fractions:

(770 + 154 + 66 + ... + 2/(31×33) × 1155 + 2/(33×35) × 1155) / 1155

To find the sum of the series, you can compute the numerator:

770 + 154 + 66 + ... + 2/(31×33) × 1155 + 2/(33×35) × 1155

This would be a lengthy calculation, and you might want to use a calculator or a computer program to perform the addition. The result of this sum will be the final answer to your question.