Dear ,
sqrt{1+2[sqrt3 +4(sqrt5 +6(sqrt7 +8(sqrt9...........infinity)))))))]}
it reads liks this
root of 1+2 root of 3 +root of 5+6root of 7+8 root of............
ur both way of expressing the que does not match as last one means
sqrt(1)+2sqrt(3)+..............
please check also as far as i am concerened it is a diversing series that means it will not converse at any value and goes on increasing with the terms .
so it might not be possible to solve it . please check the relevance of the question too.