Atividade 07

D S T Q Q S S Atividade 09 Cap 2 2 Atv 03 ao 13 08 P(1): 1 + 2 + ... + n = n ( n + 1 ) / 2 / 4 P(n+1) 1 + 2 + ... + ( n + 1 )^3 = n + 1 = { 3 y 3 ( n + y )^3 1 + 2 )^3 = n3 + 3 ( n + 1 )^3 n = 1 n + 2 + 4 falencia (n + 1)^3 = n^3 + n + 4 ) g (n + 1)^2 n^2 + 4n + 4^1 = n ( n + 1 )^2 ( n + 2 )^4/ S - P(n) : 1^3 + 2^3 + ... + [ 2 ( n y ) - 1 ]^3 = ( n v ) [ 2 ( n + 1 ) ]^3 P( n + 1 ): 1 + 2x + ... + [ 2 ( n + 1 ) - 1 ]^3 = ( n + 1 ) [ 2 ( n + 1 ) ]^3 = ( n + 1)( [ 2 ( n + 1 ) ]^3 ) 12 + 3^3 + ... + 52 ( [ n + 1) - 1 ]^3 + 17^2 12 + 3^2 + ... + (2n - 1)^2 + 2(2n-1)^2*[2(n)-1)^2 nn(2n-1)(2n+1) +2(2n+1)^2 (2n + 1)(1)[(2n-1) + 2n+1]7 falencia C(2n+1) [2]n - n + 6n + 3 ) (2n+1) C(2n3+s1+3) [2n+1)(cn+1)(n+1)/3 D S T Q Q S S 10. P(1): 1^9 = ( 1 + P )(2n+1)(C 2n)3-1 / 30 = d s 5/30 p P( n+ 1 ) 1^2+3^4 + ... + n^n = n( n+1 ) C n(1)2[ n^n) / s a 30 P( n+1 ) : 1^4 2^4 + ... + ( n + 1 )^9 (n + 1)C (2n)(C( n + 1)^3)2 + 3C n+1]-1/30 (n+1)(Ca+2+Cn+3)n [ 2(2n-2)+3Cn+1)^2+(2a+d+5)/30 n(n+1)(O2a+1)(C2n+1)+(2n+1)^2 (n+1)[(Ca+2)(Cn+3) + 2n+1)/ falencia OA(2n-1)(2+1) C(2n+1)(Cn-1)+(n+1) dn+l)(O2n+l)(O2n+3)(3n-1)3n-1+(fn+l)7 n=1 1^a+4n+3f2 n+3 = 2 + 30 ( n+1)^3 C(2n+1)(C3n+3s41+30) n + 7 (C6n+39n+3 + 9n2 + 9n+30) 70 1^a 29 4....(n+1)( n+1 )^9 1^4 + 2 + ... = s^a + (n + 1)^9 (n+1) [n(2n+1)(3n-1)+3n-1+(n+1)]9 n+1(O2 n+n)(C2n+3n-1)2+(C2n+4n+1)B 10 n+1(19o+6^n+2)3(n+1) 20 C7(n+3)[C(2n)( n + 3) / 2] (3n+9)+37]/6 + O 1:3: 2: 4+ n(n+11)( n +3) 1:3 + 2^9 + 2 n (n+2) + (n+1)( n+3) n{n^n+1}(2n+2)(n+9)/6 = C(n+1)+6/n+n+2 3iof3en (3a + (n) n(n+1)[p(n)2) + 1 + 11p n+1[n2n+2]( n +1 p)(6 = n+1(ny3n+1(2c+9)+0)/6 cn+l(ny) + 6(a-2)+ Lp) np [n+a 4]o(n+ 3/ 0 SAO DOMINGOS D S T Q Q S S 12. P(a): 1+a+... + a^n-1 = a^n-1 a-1 P(k+1): 1+a+... + a^n = a^n+1-1 a-1 q+a+...+a^n 1+a+v ; tto^n/c+o^3 a^n-1 + 4 a^a a^n-1 + a(l a-1) a^n+1 u an+1 arr-1 SAO DOMINGOS