# sultan

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# 245 Questions

 12 Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$ 11 Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$ 11 Find the sum : $\sin^{-1}\frac{1}{\sqrt{2}}+\sin^{-1}\frac{\sqrt{2}-1}{\sqrt{6}}+\sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+\cdots$ 9 How to find the sum of this : $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+ \sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+…$ 9 How to find the sum of the sequence $\frac{1}{1+1^2+1^4} +\frac{2}{1+2^2+2^4} +\frac{3}{1+3^2+3^4}+…$

# 2,703 Reputation

 +5 Let $|z|=1,$ prove that $|z^2-3z+1|\leq 5$ … +10 If $a_n = \sum^n_{r=0} \frac{(\ln10)^n}{r! (n-r)!}$ for $n \geq 0$ … +10 If $\lim_{n \to \infty} \sum^n_{k =0} \frac{nC_k}{n^k(k+3)} =ae+b$ +5 A Let f$:[-1,1] \to R, f'(0) =\lim_{n \to \infty} nf(\frac{1}{n})$ and $f(0)=0.$…

 3 Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$ 2 How does one derive these solutions to the cubic equation? 2 Finding trigonometric integral (challenging) 2 How to solve this integral easily: $\int \frac{x\cdot \sqrt[3]{x+2}}{x+\sqrt[3]{x+2}} dx$ 2 Solving $x^{\log(x)}=\frac{x^3}{100}$

# 58 Tags

 6 trigonometry × 45 2 algebra-precalculus × 66 5 integration × 24 1 logarithms × 7 3 indefinite-integrals × 6 1 combinatorics × 5 3 problem-solving × 2 1 optimization 2 calculus × 71 0 sequences-and-series × 39

# 2 Accounts

 Mathematics 2,703 rep 1527 TeX - LaTeX 101 rep