The formula c = √a^2 + b^2 represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equa
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Answer:
It means also converges.
Step-by-step explanation:
The actual Series is::
The method we are going to use is comparison method:
According to comparison method, we have:
If series one converges, the second converges and if second diverges series, one diverges
Now Simplify the given series:
Taking"n^2"common from numerator and "n^6"from denominator.
Now:
So a_n is finite, so it converges.
Similarly b_n converges according to p-test.
P-test:
General form:
if p>1 then series converges. In oue case we have:
p=4 >1, so b_n also converges.
According to comparison test if both series converges, the final series also converges.
It means also converges.
You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).
In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.
The result is
So, the second equation turned to be an equality, i.e. an equation where both sides are the same.
This implies that the system has infinitely many solutions, because every couple such that
is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.