From your last step, you can pull out the (because it has no in it), so
Spoiler:
Now pull the out of the square root to get:
Now you can see that taking gives you a limit of , (i.e. the whole thing equals ), so the series converges when , so when . You also need to check for convergence at the endpoints ( and ).
Spoiler:
For , use the alternating series test. For , compare it to .
From your last step, you can pull out the (because it has no in it), so
Spoiler:
Now pull the out of the square root to get:
Now you can see that taking gives you a limit of , (i.e. the whole thing equals ), so the series converges when , so when . You also need to check for convergence at the endpoints ( and ).
Spoiler:
For , use the alternating series test. For , compare it to .
Spoiler:
Just kidding; two nested spoilers is enough.
Thanks for the reply....i am stuck again ....I know it is a silly question but could u please tell me on what should i use the alternate series test for
I know i need to use for -1 but which equation should i use
Thanks for the reply....i am stuck again ....I know it is a silly question but could u please tell me on what should i use the alternate series test for
I know i need to use for -1 but which equation should i use
Since your series involves even powers of x, x = 1 and x = -1 give the same series. The alternating series test is not relevant because the terms do not alternate when x = -1. The comparison test, implied in the spoiler of an earlier reply, is all that is required.
Since your series involves even powers of x, x = 1 and x = -1 give the same series. The alternating series test is not relevant because the terms do not alternate when x = -1. The comparison test, implied in the spoiler of an earlier reply, is all that is required.
Mr fantastic i wanted to know where should i put in the comparison test is it to be put in the eq or in the result
Mr fantastic i wanted to know where should i put in the comparison test is it to be put in the eq or in the result
Substitute x = 1 into the original series. Then use the comparison test on the resulting series, as shown in the spoiler of an earlier reply. This will also establish what happens when x = -1 (because substituting x = -1 gives the same series).
Substitute x = 1 into the original series. Then use the comparison test on the resulting series, as shown in the spoiler of an earlier reply. This will also establish what happens when x = -1 (because substituting x = -1 gives the same series).
Substitute x = 1 in the original series we get
and
=
Is this correct????????
Last edited by zorro; December 7th 2009 at 11:42 AM.
Sorry, my bad. I didn't notice it was all even powers. In that case, -1 and 1 are the same.
In my last post i have done some step could u please check and let me know if i have done it correctly or no .....and what else do i need to do after this