limit

[stuart clark]

\(\displaystyle \lim\limits_{x\to\infty}\left(1+\frac{\sin 1}{\cos 0.\cos 1}+\frac{\sin 1}{\cos 1.\cos 2}+\dots+\frac{\sin 1}{\cos (n-1).\cos n}\right)^{\frac{1}{x}}\)

 

[galactus]

It would appear the limit is 1.

See the \(\displaystyle \frac{1}{x}, \;\ x\to \infty\).

This results in an exponent of 0.

If that were an n in the exponent, then that would be a different matter.

This problem is more observation. The x is independent of the n inside the summation.

So, it does not matter what the sum is. Anything to the zero power is 1 (except, of course, for the indeterminate what nots). See what I am getting at, big stu?.

 

[lookagain]

\(\displaystyle \lim\limits_{n\to\infty}\left(1+\frac{\sin 1}{\cos 0.\cos 1}+\frac{\sin 1}{\cos 1.\cos 2}+\dots+\frac{\sin 1}{\cos (n-1).\cos n}\right)^{\frac{1}{n}}\)

Two things:

1) I feel everything should be expressed with the same variable,
as is suggested by me in the above, to make sense.

2)What type of values are the variables supposed to be representing? Radians or degrees?

 

[stuart clark]

all angles are in degree.

 

[galactus]

As lookagain was asking, is there a typo in your problem?. Is that 1/x exponent supposed to be 1/n?.