Question

1+3/2+5/4+7/8+9/16+11/32+...=

Answer 1

Ответ:

5.5..................

Answer 2

The given expression seems to be a series where the numerators are odd consecutive numbers starting from 1, and the denominators are powers of 2 (2^n) starting from 2^0 (1).

So, the series can be written as:

1/1 + 3/2 + 5/4 + 7/8 + 9/16 + 11/32 + ...

To find the sum of this series, we need to apply the formula for the sum of an infinite geometric series:

Sum = a / (1 - r),

where:

• a is the first term (1/1 in this case)
• r is the common ratio between terms (3/2 divided by the previous term, 1/1, in this case)

So, in this case, a = 1/1 and r = 3/2.

Plugging in the values:

Sum = (1/1) / (1 - 3/2) = (1/1) / (1/2) = 2/1 = 2

Therefore, the sum of the given series is 2.