UPSC NDA Math Model Paper 3

Given that: 6

1

2

×6

1

4

×6

1

8

×6

1

16

×..... upto infinite terms
⇒6(

1

2

+

1

4

+

1

8

+.....) .....(∵am×an=am+n)
The series:

1

2

+

1

4

+

1

8

+..... is in form of infinite geometric series.
Comparing it with standard infinite G.P series, we get a = 1/2 and r = 1/2
Sum of infinite terms of a G.P, sn=

a

1−r

⇒sn=(

1 2

1− 1 2

)
⇒sn=(

1 2

1 2

)=1
⇒6(

1

2

+

1

4

+

1

8

+....)=61=6
Hence, the value of product of 6

1

2

×6

1

4

×6

1

8

×6

1

16

×..... upto infinite terms = 6