7. Find the radius and interval of convergence. (л — 2)" a) > (x + 1)" b) n 3n+1 nº 5n n=1 n=1

16. Determine the radius of convergence of the series an" when: (a) an = (logn)² (b) an = n! n=1 (c) an = 4 +3m (d) a₁ = (n!)³/(3n)! [Hint: Use Stirling's formula, which says that n!~ene" for some e > 0..] (e) Find the radius of convergence of the hypergeometric series F(a, 3₁ %; z) = 1 + a(a + 1) ... (a+n− 1)3(3+1) ··· (3 + n − 1) ¸n n!y(y + 1) (y + n − 1) n=1 Here a, 3 € C and y# 0,-1, -2,....

Q6. (1) Given log (1+t) = t-t² +t²-t ² + --- 2 3 4 valid for It

QUESTION 6 Find the interval of convergence AND find the radius of convergence. 00 3" (x-2)" Σ34 л=О (n + 1)