Question

27. [-/1 Points] DETAILS SCALCET8 11.4.019. Determine whether the series converges or diverges. MY NOTES AS 00 + 1 n + n=1 The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. The limit of the ratio of its terms and a convergent p-series is greater than 0. The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and a divergent p-series is greater than 0. The series diverges by the Limit Comparison Test. Each term is greater than that of a divergent geometric series.

Answer 1

The given series is convergence by using limit comparison test.

2 an 121 ha Givim series is a nel ng+n ntl ana ng+n limit comporison test Where nal Now using let bn= lim an bn no nto 9 2 1 nto Ito hs, mai lim n&(n+1) na+n = lim n8 (1+ tu) m9 (1+ **) = lim (H to) I+ 0 (1+B) (and) = 1 (non zero positive number) Again Series € (bn) = is convergent by pseries test, because p=871. limit comparison test the series convergent. : lim n too Me 8 h nal nal Therefore by À cott) is hat na tn :. The series converges by the timit comparison test. The limit of the ratio of its terms and convergent p-series is greater then o. .. Second option is true : a