Question

Express the following in product (π) notation. 1-1/2 ,1/2-1/3, 1/3-1/4.....1/n-1 - 1/n

Answer 1

The sequence of differences between reciprocals of consecutive integers is expressed in product notation as the product of (1/i - 1/(i+1)) for i ranging from 1 to n-1.

Step-by-step explanation:

The sequence given in the question is 1-⅒, ½-⅓, ⅓-¼,..., ⅐-⅑. This sequence represents a series of differences between the reciprocals of consecutive integers. To express this sequence in product notation (π), we need to identify a patter that applies to all terms in the product. In this particular case, we are subtracting the reciprocal of the next integer from the current one, starting at 1 and going up to n.

The general term for this sequence can be written as (1/i) - (1/(i+1)) where i starts at 1 and increments up to n-1. So in product notation, we can express the sequence as:

`Π_(i=1)^(n-1)  [ (1/i) - (1/(i+1)) ]`

Here, the term inside the brackets represents the general term in the sequence, while the product symbol (π) indicates that we take the product of all such terms for i ranging from 1 to n-1.