Sequences and S...

The sum $$\dfrac{1}{1+1^{2}+1^{4}}+\dfrac{2}{1+2^{2}+2^{4}}+\dfrac{3}{1+3^{2}+3^{4}}+...+\dfrac{99}{1+99^{2}+99^{4}}$$ lies between

Find : $$12,15,21,24,30,33 , ? , ?$$

Find : $$13,23,43,83,163 , ?$$

Total number of divisors of $$N=3^{5}.5^{7}.7^{9}$$ that are of the form $$4n+1,\ n\ \ge 0$$ is  

Find the missing number :

$$23,29,47,75 , ?$$

$$16,40,100,250 , ?$$

Find the missing number

Find the missing number.

The sum of $$\displaystyle \sum^{\infty}_{n=1}\tan^{-1}\left(\dfrac {2}{n^{2}+n+4}\right)$$ is equal to-