求数列最大项的问题,问题如图所示
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an = (n+2) (7/8)^n
consider
f(x)=(x+2).(7/8)^x
f'(x) =(7/8)^x + (x+2).ln(7/8).(7/8)^x
f'(x)=0
(7/8)^x + (x+2).ln(7/8).(7/8)^x =0
1 + (x+2)ln(7/8) =0
x = -(1+2ln(7/8))/ln(7/8)
=5.49
a4 =(4+2) (7/8)^4 =14406/4096 =3.5171
a5 = (5+2) (7/8)^5 = 117649/32768=3.59
a6=(6+2)(7/8)^6 = 941192/262144=a5
max an = a5 or a6
consider
f(x)=(x+2).(7/8)^x
f'(x) =(7/8)^x + (x+2).ln(7/8).(7/8)^x
f'(x)=0
(7/8)^x + (x+2).ln(7/8).(7/8)^x =0
1 + (x+2)ln(7/8) =0
x = -(1+2ln(7/8))/ln(7/8)
=5.49
a4 =(4+2) (7/8)^4 =14406/4096 =3.5171
a5 = (5+2) (7/8)^5 = 117649/32768=3.59
a6=(6+2)(7/8)^6 = 941192/262144=a5
max an = a5 or a6
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