I'm guessing the series is supposed to be
By the ratio test, the series converges if the following limit is less than 1.
The first
terms in the numerator's denominator cancel with the denominator's denominator:
also cancels out and the remaining factor of
can be pulled out of the limit (as it doesn't depend on
).
which means the series converges everywhere (independently of
), and so the radius of convergence is infinite.
Answer:
f(1) is 1, just look at the x-value provided in the parenthesis. f(1) means function value at x = 1, and the graph shows that at x = 1, y = 1.
Answer:
345
Step-by-step explanation:
We can solve this problem by two equations. Our variables will be the following:
is the amount to be multiplied
and 
is the amount that should be obtained by multiplying by 43
Thus our <u>first equation</u> is:
But the problem tells us that there was an error and the number was multiplied by 34, so the result failed by 3105, thus the <u>second equation</u> is as follows:
By multiplying the quantity by 34, an amount is obtained that differs from 3105 from what it would have been obtained if multiplied by 43.
Now we are going to <u>replace the first equation in the second one </u>(
):
And clear to find x:
The number that jimmy was supposed to multiply by 43 is 345.
