Question

Activity :- Find the value of 2⁰, 2¹, 2², 2³, 2⁴ by paper

folding and pasting. Materials Required:​

Answer 1

Answer:

Step-by-step explanation:

There is really no need for a long answer. Visual approach.

The representation of  xn  in  basex  is always a one followed by  n  zeroes. So if we add all of them starting at  0  we get  n+1  ones in  basex .

If we dont add the first  (20) , as in your question, we only get n ones followed by one zero. Thats 12 ones and a zero, which is  8190  in decimal.

Special case in  base2 :

Adding 1 to a number that only consists of the highest digit  (x−1 in basex ) all digits will be zero, lead by a one.

In the special case for base 2 the one is the highest digit, therefore adding all and then adding 1 will give us the next power:  2(n+1)  

sum(2i,0,n)+1=2(n+1)  

For  n=12  we get  213−1=819

Answer 2

sorry mine was wrong so I did edited i

sorry