Sequences and S...

The sum of the series $$1^{3}+3^{3}+5^{3}+....$$ upto $$20$$ terms is

The $$nth$$ term of the series $$4, 14, 30, 52, 80, 114, ...$$ is

The sum of $$(n+1)$$ terms of $$\frac { 1 }{ 1 } +\frac { 1 }{ 1+2 } +\frac { 1 }{ 1+2+3 } +.......is$$

The three digits in 10! are:

The sum of the series $$\dfrac {5}{1 \cdot 2 \cdot 3}+\dfrac {7}{3 \cdot 4 \cdot 5}+\dfrac {9}{5 \cdot 6 \cdot 7}+....$$ is

If the sum of the series $$1+\dfrac{3}{x}+\dfrac{9}{x^{2}}+\dfrac{27}{x^{3}}+....$$ to $$\infty$$ is a finite number then 

The value of $$\sum_{n=1}^{\infty}\dfrac{1}{(3n-2)(3n+1)}$$ is equal to $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are relatively prime natural numbers. Then the value of $$(p^2+q^2)$$ is equal to

If $$p:q:r=1:2:3\;then$$ $$\sqrt {5{p^2} + {q^2} + {r^2}} $$ is equal to: 

The sum $$1 + 3 + 7 + 15 + 31 +  \ldots $$ to $$n$$ term is 

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