设f(n)=1n+1+1n+2+1n+3+…+13n(n∈N*),则f(n+1)-f(n)=( )
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/05/07 13:26:12
设f(n)=
+
+
+…+
(n∈N
1 |
n+1 |
1 |
n+2 |
1 |
n+3 |
1 |
3n |
根据题中所给式子,得f(n+1)-f(n)
=
1
(n+1)+1+
1
(n+1)+2+
1
(n+1)+3+…+
1
3(n+1)-(
1
n+1+
1
n+2+
1
n+3+…+
1
3n)
=
1
3n+1+
1
3n+2+
1
3n+3-
1
n+1
=
1
3n+1+
1
3n+2−
2
3n+3
故选C.
=
1
(n+1)+1+
1
(n+1)+2+
1
(n+1)+3+…+
1
3(n+1)-(
1
n+1+
1
n+2+
1
n+3+…+
1
3n)
=
1
3n+1+
1
3n+2+
1
3n+3-
1
n+1
=
1
3n+1+
1
3n+2−
2
3n+3
故选C.
设f(n)=1n+1+1n+2+1n+3+…+13n(n∈N*),则f(n+1)-f(n)=( )
求证f(n+1)*f(n-1)-f(n)*f(n) = (-1)^n,f(n)是费波纳茨数列
设f(n)=1/(n+1)+1/(n+2)+……+1/(2n) (n∈N新),那么f(n+1)-f(n)等于(1/(2n
设f(n)=1n+1+1n+2+…+12n(n∈N),则f(n+1)-f(n)= ___ .
f(n)=1/(n+1)+1/(n+2)+…+1/(2n-1)+1/(2n) (n≥2,n∈N*)
设f(n)=1/(n+1)+1/(n+2)+...+1/2n,则f(n+1)-f(n)等于()
如果f(n)=1/(n+1)+1/(n+2)+```1/2n (n属于N*) 那么f(n+1)-f(n)=
设f(n)=1+1/2+1/3+…+1/2n 则f(n+1)-f(n)=?
f(n)=1/(n+1)+1/(n+2)+1/(n+3)……+1/2n (n∈N*),f(n+1
设定义在N*上的函数f(n)=n(n为奇数);f(n)=f(n/2)(n为偶数),an=f(1)+f(2)+f(3)+·
设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)
设f〔n〕=(n+1)分之一+(n+2)分之一+……+2n分之一 则f(n+1)-f(n)=