Evaluate:lim [ 1+nth root{1^n +2^n} + nth root{2^n+3^n} + .......................+nth root{(m-1)^n +m^n}]

where m,n approach infinity.......

Sorry couldnt write in proper way becoz new to me.........

plzzz help ASAP

help..................

Take the larger of the two no.s in the series outside the root. So equation becomes

1+ 2 * nth root {1 +(1/2)^n} + 3 * nth root {1 + (2/3)^n}...................m * nth root {1 + (m-1/m)^n}

Lim n->inf =  1+2 + 3....+m

= m(m+1)/2

Lim m-> inf gives the answer infinity. Is it right?

NO...........

answer is 1/2

Srry about my solution then, I did have a doubt in that. I will get back to you with a solution ASAP. But its strange that the answer is less than 1. :\

What you actually needed was something else so my answer is right but to know what you needed see this: http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212489