大学数学基础(1)04-第二章高等数学预备知识随堂测验答案

第二章高等数学预备知识随堂测验答案第一讲合并与化简

1.

c o s x c o s x x

n

2

去掉分母得：

c o s x 1

_ _ _ _ _ _ .

(A ) 1 (co s x 1) (co s x co s x 1)

2

(B ) 1 (co s x 1) (co s x c o s x 1)

2

(C ) 1 co s x c o s x x

2 1

(D ) 1 c o s x c o s x

2

n 1 x

答案：B

解c o s x co s x

2

c o s x 1 c o s x

1

(co s x 1) (co s x 1)(co s x 1) (co s x 1)(co s x co s x 1)

x 1) 2

2

c o s x 1

c o s x c o s x

2

(co s x 1) (co s x 1)(co s x 1) (co s x 1)(co s x c o s x 1)

2

n 1 n 2

(co s x 1)(co s x c o s x 1)

(co s x 1) 1 (co s x 1) (co s x c o s x 1)

2

故

c o s x co s x x

n

2

c o s x 1

2 1 n 2 x

=1 (co s x 1) (co s x c o s x 1) x c o s1) 2.

1 1

_ _ _ _ _ _ .

已知x ，则x

n n

2

3 1 5

4 n 1

1 1 1 1

答案：C (A ) 1 (B ) 1

2 2 n 1 2 2 n 1

1 1 1 1

(C ) 1 (D ) 1

2 2 n 1 2 2 n 1

1 1 1 1

解=，

4 1 2 2 1 2 1

n n n

2

1 1 1 1 1 1 1 1 故x

n

1 1

2 3 3 5 2 n 1 2 n 1 2 2 n

1

3.

n

合并乘积得：(1 x )(1 x )(1 x ) ) _ _ _ _ _ _ .

2 4

n 1 n 1 n 1 n

1 x 1 x 1 x 1 x

2 2 2 2 1

(A ) (B)(C) (D )

1 x 1 x 1 x 1 x 答案：A

n (1 x )(1 x )(1 x )

)

2 4

n (1 x )(1 x )(1 x )(1 x )

)

2 4

1 x

(1 x )(1 x )(1 x )

2 2 4

1 x 1 x

n n n n 1

(1 x ) (1 x ) 1 ( x ) 1

x

2 2 2 2 2

1 x 1 x 1 x

4.

n

1

设x ，则数列 { x } _ _ _ _ _ _

n n

n

k k 1

(A ) 单调递减但无界(B)单调递减且有界

(C) 单调递增但无界(D) 单调递增且有界

答案：D

解x

n

n

1 1 1 1

n k n 1 n 2 n n

k 1

x n

1

n 1

k 1

1

(n 1)

k

1 1 1

(n 1) 1 ( n 1) 2 ( n 1) ( n 1)

1 1 1 1

则x x = 0，故 { x }单增

n 1 n n

2 n 1 2 n 2 n 1 2 (2n 1)(n 1)

n n

1 1 1

又x 1，所以 { x }有上界，下界为x .

n n 1

n k n

2 k 1 k 1

5.

x x x x

化简：c o s c o s c o s_ _ _ _ _ _ .

2 n 1 n

2 2 2 2

si n x sin x c o s x si n x (A ) (B)(C) (D)

x x x x n 1 n n n

2 sin 2 sin 2 sin 2 c o s

n n n n

2 2 2 2

答案：B

解

x x x

c o s c o s c o

s

2 n 1 n

2 2 2

2

x x x x x

c o s c o s c o s 2 sin

2 n 1 n n

2 2 2 2 2

x

2 sin

n

2

x x x x x x x

c o s c o s

2 n 1 n 1 2 n 2

2 2 2 2 2 2 2

x x

2

2 sin 2 si n

n n

2 2

x x

c o s sin

si n x

2

x x

n 1 n

2 sin 2 sin

n n

2 2

第二讲常用求和方法1

1.

2

已知a ，则数列{a }的前n项和为______ .

n n

1 2

4 n n 4 n n

(A) (B)(C )(D )

n 1 n 1 n 1 n 1

答案：A