Question

please answer both!!!
(1 point) Use the binomial series to find the first 5 nonzero terms of the power series centered at x = 0 for the following function and then give the open interval of convergence for the full power series. 1 f(x) = (5 + x)5 f(x) = + + + + ... + (Give your The open interval of convergence is: answer in interval notation.)

Answer 1

Sol 5 {1+ ] 55 I- وا 2+ 2! 8! 35 3! =i+t?)'=1-49+(69=149+(294 Ginen fuction for (5+705 fo) ㅗ 55(1+2) fo (+97" 0(0+1),? nontoln+2),}+ [i-a scoot a + szem- sub-2a3+ 5.6.7.8 in L ---) 3 a2 -Iult 14, from 628 -5cuar open interud of convergence is (-5,5) Giuen fuush fit) = f 1 - 4 dn. ㅗ 2 + 625 = 3 625 १ + x² 크 625 14 nu 625 3125 2!+ + + 7 + 625 3125 625 625 The expannian is valid only of 1711 -1<< Phe HET - GU9) 8 GBEN no = 스 HE 030 90+1 E GODEAN = e Gor (-OSE neo 90+1 dre 8W St dt = HE no to E COMED+2 90+2 n=0 9n+2 f(t)=2 E tc C-12h n=0 90+2 90+2 E IGDO f(t) = c + ?+ E 38 nool 90+2 29 20 + 38 t" 29 e+ 36 + fitl=ct El 20 E 2 20 -- + 38 + 62 f(t) = C+ + EF 28 20 The expansion à valid of 1621 -KECI (-۱,۱) " The open interval of convergene &