Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 78
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=n\left(1-\cos \frac{1}{n}\right)$$
Problem 79
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\sqrt{n} \sin \frac{1}{\sqrt{n}}$$
Problem 80
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\left(3^{n}+5^{n}\right)^{1 / n}$$
Problem 81
Make up an infinite series of nonzero terms whose sum is a. 1 b. \(-3 \quad\) c. 0
Problem 81
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\tan ^{-1} n$$
Problem 82
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\frac{1}{\sqrt{n}} \tan ^{-1} n$$
Problem 83
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\left(\frac{1}{3}\right)^{n}+\frac{1}{\sqrt{2^{n}}}$$
Problem 83
Show by example that \(\Sigma\left(a_{n} / b_{n}\right)\) may diverge even though \(\Sigma a_{n}\) and \(\Sigma b_{n}\) converge and no \(b_{n}\) equals 0
Problem 84
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\sqrt[n]{n^{2}+n}$$
Problem 85
Which of the sequences \(\left\\{a_{n}\right\\}\) converge, and which diverge? Find the limit of each convergent sequence. $$a_{n}=\frac{(\ln n)^{200}}{n}$$
