Albert said:$x_1+x_2=x_2+x_3=x_3+x_4=x_4+x_5=--------=x_{998}+x_{999}=1$
$x_1+x_2+x_3+x_4+x_5+--------+x_{999}=999$
find :
$x_1+x_3+x_5+x_7+---+x_{999}=?$
The pattern in this expression is that we are adding all odd numbers from x_1 to x_999. This can also be written as the sum of all odd terms in the series x_1 to x_999.
To solve this expression, we need to first find the value of x_1, x_3, x_5, and so on until x_999. Then, we can simply add all these values together to get the final answer. Alternatively, we can use the formula (n/2)(2a + (n-1)d) where n is the number of terms, a is the first term, and d is the common difference to find the sum of the series.
Yes, we can rewrite this expression in sigma notation as ∑_(i=1)^999 x_(2i-1), where i represents the term number and 2i-1 represents the odd term in the series.
If x_1 = 1 and x_999 = 999, then the value of the expression would be 250,000. This can be calculated by using the formula (n/2)(a + l) where n is the number of terms, a is the first term, and l is the last term in the series.
This type of expression is commonly used in mathematics and physics to find the sum of a series of terms with a specific pattern. It can also be used in computer programming to calculate the sum of odd numbers or in financial calculations to find the total cost or revenue over a period of time.