设函数f(x)满足2f(n+1)=2f(n)+n,f(1)=2,则f(5)=()A.6B.6.5C.7D.7.5-高二数学

题目简介

设函数f(x)满足2f(n+1)=2f(n)+n,f(1)=2,则f(5)=()A.6B.6.5C.7D.7.5-高二数学

题目详情

设函数f(x)满足2f(n+1)=2f(n)+n,f(1)=2,则f(5)=(  )
A.6B.6.5C.7D.7.5
题型:单选题难度:偏易来源:不详

答案

∵函数f(x)满足2f(n+1)=2f(n)+n,f(1)=2,
∴f(2)=f(1)+class="stub"1
2
=1+class="stub"1
2
=class="stub"3
2

f(3)=f(2)+1=class="stub"3
2
+1
=class="stub"5
2

f(4)=f(3)+class="stub"3
2
=class="stub"5
2
+class="stub"3
2
=4,
f(5)=f(4)+2=4+2=6.
故选:A.

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