Vn+n-1 Vn1 -1 Evaluate Lim n-700
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Vn+n-1 Vn1 -1 Evaluate Lim n-700

JEE/Engineering Exams
Maths
Solution
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( l=lim _{n rightarrow infty}left(frac{sqrt{n^{2}+n}-1}{n}right)^{2 sqrt{n^{2}+n}-1} ) ( l=lim _{n rightarrow infty}left(sqrt{1+(n)}-left(frac{1}{n}right)^{2 sqrt{n^{2}+n}-1}(=1)right. ) ( log l=lim _{n rightarrow infty} 2 sqrt{n^{2}+n-1} log left(sqrt{1+frac{1}{n}}-frac{1}{n}right) ) ( log l=frac{2 lim _{n rightarrow infty} frac{frac{1}{2}left(frac{1}{n^{2}}right)}{1}}{frac{1}{-k^{2}} cdot frac{1}{2 times 2} cdot 2 pi} ) ( =2 times frac{1}{x} ) ( log l . quad=quad 1 ) ( l=e^{1} )
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