Question

c0+2c1+4c2+...........+cn.2n=243 then n=

Answer 1

Answer:

ANSWER

Fact: (1+x)

n

=

n

C

0

+

n

C

1

x+

n

C

2

x

2

+

n

C

3

x

3

+............+

n

C

n

x

n

Substitute x=2 in above identity

(1+2)

n

=

n

C

0

+

n

C

1

(2)+

n

C

2

(2)

2

+

n

C

3

(2)

3

+............+

n

C

n

(2)

n

∴

n

C

0

+2⋅

n

C

1

+4⋅

n

C

2

+8⋅

n

C

3

+........+2

n

⋅

n

C

n

=3

n

Step-by-step explanation:

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