Question

已知数列{Tn},Tn= 3/(2^(n+2)+3/2^n-6),证明T1+T2+T3+···

Answer 1

令Cn=2^(n+2)+3/2^n ,

所以C(n+1)-Cn=2^(n+3)+2/2^(n+1) - 2^(n+2) - 2/2^n= 2^(n+2) -1/2^n >0

所以C(n+1)>Cn,T(n+1)