<span>The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + â‹Ż is a divergent series. The nth partial sum of the series is the triangular number
{\displaystyle \sum _{k=1}^{n}k={\frac {n(n+1)}{2}},} \sum_{k=1}^n k = \frac{n(n+1)}{2},
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting</span>
Multiply denominator and numerator of fraction by conjugate (2√7 -6)
=
Expand using distributive property
=
Collect like terms to simplify
=
-9
Because if you have negative three and it drops 6 then it becomes negative 9
Answer: f(n+1) = (n - 1)/(n + 2)
Explanation:
f(x) = (x - 2)/x+1
Find f(n+1) simply replace x by (n+1)
f(n+1) = (n + 1 - 2)/(n + 1 + 1)
= (n - 1)/(n + 2)
Answer:
Step-by-step explanation:
step 1
Find the area of the circle
The area of the circle is equal to
we have
substitute
step 2
we know that
The area of a circle subtends a central angle of 2π radians
so
using proportion
Find out the area of a sector with a central angle of 8 π/11 radians
