Question

数学数列求通项a1+2a2+3a3+...+nan=2^n

Answer 1

a1+2a2+3a3+...+nan=2^n

a1+2a2+3a3+...+nan+（n-1)an-1=2^(n-1) (n-1>0,即n>1)

相减

n*an=2^(n-1)

an=2^(n-1)/n (n>1)

n=1时,a1=2

2 n=1

an=

2^(n-1)/n n>1