若数列{bn}是等差数列,且bn=sn/(n+c),求常数c

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若数列{bn}是等差数列,且bn=sn/(n+c),求常数c若数列{bn}是等差数列,且bn=sn/(n+c),求常数c若数列{bn}是等差数列,且bn=sn/(n+c),求常数cSn=bn(n+c)

若数列{bn}是等差数列,且bn=sn/(n+c),求常数c
若数列{bn}是等差数列,且bn=sn/(n+c),求常数c

若数列{bn}是等差数列,且bn=sn/(n+c),求常数c
Sn=bn(n+c)
n=1
b1=S1=b1(1+c)
1+c=1
c=0

c=0

因为Sn为数列bn的和所以b=1为第一项即S1 SI是第一项

Sn=bn(n+c)
Sn-1=bn-1(n-1+c)
Sn-Sn-1=bn=bn-1+(bn-bn-1)*(n+c)
所以bn-bn-1=(bn-bn-1)*(n+c)
所以bn-bn-1=0或者n+c=1
当bn=bn-1时为常数数列,则c=0
当n+c=1时,即c=1-n时,bn=bn-1=0不成立
所以c=0

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