Question

这道题怎么做，我做的对吗

Answer 1

（1) an= 2n + 3^n; Sn= 2(1+n)*n/2 + 3*(1-3^n)/(1-3)= n*(n+1) - (3 - 3^(n+1))/2。
（2) an= 1/(1+2+……+n) = 2/n*(n+1)= 2*(1/n - 1/(n+1) );
Sn= 2(1- 1/(n+1) )= 2n/(n+1);
(3) an= n* (0.5)^n; Sn= 1* (0.5)^1 + 2*(0.5)^2 + 3*(0.5)^3 + ……+ (n-1)*(0.5)^(n-1) + n*(0.5)^n;
0.5Sn= 1*(0.5)^2 + 2*(0.5)^3 + 3*(0.5)^4 + ……+ (n-2)*(0.5)^(n-2) + (n-1)*(0.5)^n + n*(0.5)^(n+1)
Sn - 0.5 Sn= (0.5)^1 + 1*(0.5)^2 + (0.5)^3 +……+ (0.5)^n - n*(0.5)^(n+1)
= 0.5*( 1- (0.5)^n )/ (1-0.5) - n*(0.5)^(n+1)
Sn= 2*(1- (0.5)^n ) - n*(0.5)*n = 2 - (n+2)*(0.5)^n