1is it 1/2 power 2 power n
or 1/2 power 2n??
12 Answers
1that simply means (1+ 1/2)(1+1/22)(1+1/24)(1+1/28)(1+1/216).... infinity = 1+1/2 + 1/22 + 1/23 +1/24....... infinity now i think you can find the sum to these infinite no. of terms ... and the answer comes out to be 2
i think i should explain too
consider the expansion of the above series
when we start to multiply if we take 1 from every bracket so we have 1*1*1* =1 so the first term becomes 1
when we take 1/2 from the first and 1 from all other brackets we shall get 1/2 ...here's the second term too
when we shall take 1/2 from the first bracket and 1/22 from the second one ...we shall have 1/23 as the third term....and if you continue you will get a infinite G.P. with first term as 1 and common ratio as 1/2 ...so the answer is 2
3its qiite simple shriya ....... take lcm of all terms ..... and luk at the numerater ....
multiply nd divide by 2-1 ........... solve for n terms and then apply limit to infinty ,,,
62(1+ 1/2)(1+1/22)(1+1/24)(1+1/28)(1+1/216).... infinity
now divide and multiply by 1-1/2
use (a-b)(a+b) = a2-b2
and then enjoy ;)
62oh ok :)
i din realize what you meant by dividing and multiplying by 2-1!