Question

f A = | 1 ,1 0| and A 2 = I, then a =?​

Answer 1

Answer:

Correct option is

D

1000

1

We have, f:N→R such that f(1)=1

And f(1)+2f(2)+3f(3)++nf(n)=n(n+1)f(n),∀n≥2

Clearly, f(1)+2f(2)=2(2+1)f(2)

⇒f(1)=6f(2)−2f(2)

⇒f(1)=4f(2)

⇒f(2)=

4

f(1)

=

4

1

Similarly, f(1)+2f(2)+3f(3)=3(3+1)f(3)

⇒1+

2

1

+3f(3)=12f(3)

⇒9f(3)=

2

3

⇒f(3)=

6

1

and f(1)+2f(2)+3f(3)+4f(4)=4(5)f(4)

⇒1+

2

1

+

2

1

=16f(4)

⇒f(4)=

16

2

=

8

1

In general, f(n)=

2n

1

∴f(500)=

1000

1