Scroll to see replies
Spoiler
Spoiler
Spoiler
Spoiler
\displaystyle\lim_{n\to \infty} \left( \int^1_0 \frac{dx}{1+x^n} \right)^n=\lim_{n\to \infty}\left(1-\frac{1}{n+1}+\frac{1}{2n+1}-\frac{1}{3n+1}+...\right)^n\\& \displaystyle=\lim_{n\to \infty}\left(1-\left(\frac{1}{n}-\frac{1}{2n}+\frac{1}{3n}+... \right) \right)^n \\& =\displaystyle\lim_{n\to \infty}\left(1-\frac{1}{n}\int^1_0 \frac{dx}{1+x}\right)^n \\& =\displaystyle\lim_{n\to \infty}\left(1-\frac{\ln2}{n}\right)^n \\& =\displaystyle\frac{1}{2}
& =\displaystyle\lim_{n\to \infty}\left(1-\frac{\ln2}{n}\right)^n \\& =\displaystyle\frac{1}{2}
\displaystyle\lim_{n\to \infty}\left(1-\frac{\ln2}{n}\right)^n & =\displaystyle\frac{1}{2}
32 Solution
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong71
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong71