Question

数列与不等式证明an=[（2n+4）乘3的n-1次方]/n,证明sn大于3的n次方再问一个。证明（1/a+1/b+1/c

Answer 1

一：用数学归纳法证明：a1=S1=6>3^1,

假设当n=k时Sk=a1+a2+······ak>3^k,

则当n=k+1时：a1+a2+·····ak+a(k+1)>3^k+a(k+1)

=3^k+[(2k+6)*3^k]/(k+1)

=3^k[3+4/(k+1)]>3^(k+1)成立

二：提示：用柯西不等式证明,不好写就不打了