Question

Calculus 2. Please use best handwriting as possible thank you!

Determine if the scrics (-1) 21 is convergent or divergent: 71 14) State a series that is conditionally convergent and justify your answer: 15) Verify that the scrics 42 converges and find the sum: - n(n+2)

Answer 1

0:1) E (-1)" 21 21 nel I. sle nal 21 E c.in n=1 n z (-1)" is known as series ne) -ho (no) it is E (-1) n 1) no > 0 coin hoz -1 therefore 21 § (-1)" 2.21 Elu (2)] nal Henic 18 W 21 (-1) -21 ln(2) n 7 nal M8 21 (-1) -21 en (2) h --14:1560

9-2) E (-1)" 21 h nal by rast Ratio test lim Mac anti an lim h - | [1]** (21) (-1) (28) lim nti-h n fo ht dim n - LI) ( nti (-1) lim a م م * ht Answar is negative which is c1 . Aboven series is convergent series.

42 he) nch+2) By radio test ant an If no tare a lim 42 (n+1) entite) 42 henta) 42 nch+2) (n+1)(n+3) 42 lim lim n - ? n(n+2) (nt I) (n+3) lim ha n2f2n n2+ 3nt nt 3 시 2

Above series 3 Convention Convergent 21 쿼리 (ht2) BW Nem 4의 M8 42 ncht2) 의 This 13 a kkscoping series 민 (금- 는 리 nt2 님 ) - (-3) + 리, 5 十 nal t t (7) +목) (-3) + + C 65 2 42 89 2 nChr2) nal