Lt  1+2+3+4+.....+n/(square of n)
n tends to infinity
 

Asked by raoss1967 | 17th Jul, 2015, 05:42: PM

Expert Answer:

L e t space x equals stack l i m with n rightwards arrow infinity below fraction numerator 1 plus 2 plus 3 plus 4 plus... plus n over denominator n squared end fraction W e space k n o w space t h a t space 1 plus 2 plus 3 plus 4 plus... plus n equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction T h u s comma space stack l i m with n rightwards arrow infinity below fraction numerator 1 plus 2 plus 3 plus 4 plus... plus n over denominator n squared end fraction equals stack l i m with n rightwards arrow infinity below fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 n squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals stack l i m with n rightwards arrow infinity below fraction numerator open parentheses n plus 1 close parentheses over denominator 2 n end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half stack l i m with n rightwards arrow infinity below fraction numerator open parentheses n plus 1 close parentheses over denominator n end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half stack l i m with n rightwards arrow infinity below open parentheses 1 plus 1 over n close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half plus stack l i m with n rightwards arrow infinity below 1 over n space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half plus 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half

Answered by Vimala Ramamurthy | 18th Jul, 2015, 10:21: PM