Question

Find the sum of the following series 12+6+3+1.5+… to 10 terms.

Answer 1

Answer:

24

Step-by-step explanation:

Let the series be

S

1

=

∑

i

=

1

→

∞

a

i

=

12

+

6

+

3

+

...

.

+

a

n

+

...

+

a

∞

Consider the generic case: of

S

2

Let k be any constant

Let r be the geometric ratio

Then

a

i

=

k

r

i

Then

S

2

=

k

r

1

+

k

r

2

+

k

r

3

+

...

+

k

r

n

......... ( 1 )

Note that you could have

k

r

0

+

k

r

1

+

k

r

2

+

...

+

k

r

n

Multiply (1) by r giving:

r

S

2

=

k

r

2

+

k

r

3

+

k

r

4

+

...

+

k

r

n

+

k

r

n

+

1

......... (2)

(2) - (1) ginves:

r

S

2

−

S

2

=

−

k

r

1

+

k

r

n

+

1

S

2

=

k

r

(

r

n

−

1

)

r

−

1

........( 3 )

Notice that the number sequence is reducing implying the

r

<

1