A number theory problem by tanveen dhingra

Number Theory Level pending

Find the value of 1+ 1/2 + 1/4+1/8+1/16+................. ∞


The answer is 2.

Tanveen Dhingra by tanveen dhingra , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Tanveen Dhingra
Oct 5, 2014

Let us assume 1+ 1/2 + 1/4+1/8+1/16+................. ∞ to be x. x = 1+ 1/2 + 1/4+1/8+1/16+................. ∞ Taking 1 on LHS x-1 = 1/2 + 1/4+1/8+1/16+................. ∞
Now, take 2 common from 1/2 + 1/4+1/8+1/16+................. ∞ So, it will become 1/2( 1+ 1/2 + 1/4+1/8+1/16+................. ∞ ) and as 1+ 1/2 + 1/4+1/8+1/16+................. ∞ = x, we will replace it by x. So, x-1 = 1/2x x-1/2x=1 1/2x=1 x=2 Therefore the answer is 2.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Lol too long

Mardokay Mosazghi - 5 years, 6 months ago

Log in to reply

Yeah I know I could have done it by GP but at that time I had no idea of GP so I used an alternate method. :p

tanveen dhingra - 5 years, 6 months ago
Ayush Choubey
Dec 1, 2014

Comon ratio = 1/2

S(infinity) = a / 1-r = 1 1 − 1 / 2 \frac{1}{1-1/2} = 1 1 / 2 \frac{1}{1/2} = 2 \boxed2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...