True or false: if (x) converges, then every subsequence (x) is Cauchy. n=] k=1
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- Suppose that an(x – 6)" converges for x = 10. At which of the points (a)-(d) must it also converge? (a) x = 8 (b) x = 11 (c) x = 3 (d) x = 02n Let an = Зп + 1 (a) Determine whether {a,} is convergent. (b) Determine whether>an is convergent.Let (xn) and (yn) be bounded sequences. Show that there exists a common subsequence that each sequence converges along- that is (xnk) and (ynk) both converge..
- Assume (fn) and (gn) are uniformly convergent sequences of functions. (b) Give an example to show that the product (fngn) may not converge uniformlyDetermine whether the sequance in images is convergent ( find the value it convengers), divergent, divergent to ∞ or -∞ for any fixed k≠0+ 1 4) Show that converges/diverges n= (1)