n 13. lüm (-m** ***** 2is equal t 1...
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n 13. lüm (-m** ***** 2is equal t 13. lim ... is equal to 2x n 1- 27 1- na (a) 0 (b) - (d) None of these

JEE/Engineering Exams
Maths
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( left.begin{array}{rl}lim _{n rightarrow infty} mid frac{1}{1-n^{2}}+frac{2}{1-n^{2}}+cdots & frac{n}{1-n^{2}}end{array}right) ) ( begin{aligned} frac{1+2+3+cdots}{1-n^{2}} &=frac{n(n-1)}{(1-n)(1+n)}=frac{-n}{2(1+n)} &=frac{-1}{2} frac{1}{left(frac{1}{n+1}right)} therefore lim _{n rightarrow infty} frac{1}{2} frac{1}{left(frac{1}{n}+1right)} &=frac{1}{2} frac{1}{0+1}=frac{-1}{2} end{aligned} )
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