Sequences and S...

The sum of infinity of the series $$\dfrac{1}{1} + \dfrac{1}{1 + 2} + \dfrac{1}{1+2+3}+$$______ is equal to:

A series is given as: $$4+7+10+13+16+.....$$ Find the sum of the series up to $$10$$ terms.

If $$a_n=n(n!)$$, then $$\displaystyle\sum^{100}_{r=1} a_r$$ is equal?

If $$a_{1}=a_{2}=2,a_{n}=a_{n-1}-1(n > 2)$$ then $$a_{5}$$ is ?

The sum of the series $$1+\dfrac{1}{4\times 2!}+\dfrac{1}{16\times 4!}+\dfrac{1}{64\times 6!}+....\infty$$ is?

The sum of the series $$1+2.2+3.2^{2}+4.2^{3}+5.2^{4}+.+100.2^{99}$$ is  ?

Sum  of first n terms of the series $$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{{15}}{{16}} + ....$$ is equal to 

If $${ S }_{ n }=\overset { n }{ \underset { r=1 }{ \Sigma  }  } { t }_{ r }=\dfrac { 1 }{ 6 } n\left( 2{ n }^{ 2 }+9n+13 \right) $$, then $$\overset { n }{ \underset { r=1 }{ \Sigma  }  } \sqrt { { t }_{ r } } $$ equals ?

The number of zeroes, at the end of $$50!$$, is

The sum of the series $$1+2(1+1/n)+3(1+1/n)^2+....\infty$$ is given by?