Question

On dividing x3 + 3x2
+ 3x +1 by x+r we get remainder:
(а) -n 3+ за 2-3n +1
(b) n - 3n 2 + 3n +1
(c) - п - 3n 2- 3n -1
(d) -n3 + 3n2 – 3n
-1​

Answer 1

Step-by-step explanation:

Prove that the expansion of (1−x

3

)

n

may be put into the form (1−x)

3n

+3nx(1−x)

3n−2

+

1.2

3n(3n−3)

x

2

(1−x)

3n−4

+…

Q2

If D

r

=

∣

∣

∣

∣

∣

∣

∣

∣

r−1

(r−1)

2

(r−1)

3

n

2n

2

3n

3

6

4n−2

3n

2

−3n

∣

∣

∣

∣

∣

∣

∣

∣

then

r=1

∑

n

D

r

=

Q3

Let △a=

∣

∣

∣

∣

∣

∣

∣

∣

a−1

(a−1)

2

(a−1)

3

n

2n

2

3n

3

6

4n−2

3n

2

−3n

∣

∣

∣

∣

∣

∣

∣

∣

. Then ∑

a−1

n

△a is equal to