Question

112^n+3−(121)^n+2 / [(1331)^n+1]

Answer 1

Explanation:

Formula for sum of infinite geometric series is

S

∞

=

a

1

1

−

r

;

−

1

<

r

<

1

We have a geometric series :

1

3

+

1

9

+

1

81

+

...

...

...

First we know

a

1

=

1

3

(the first term)

Second: Identify

r

, we know

r

=

a

2

a

1

or

r

=

a

n

a

n

−

1

r

=

1

9

1

3

⇔

1

9

⋅

3

1

=

1

3

r

=

1

3

Substitute into the formula

S

∞

=

1

3

1

−

1

3

=

1

3

2

3

=

(

1

3

)

⋅

(

3

2

)

S

∞

=

1

2