Sequences and S...

It is known  that $$\sum\limits_{r = 1}^\infty  {\frac{1}{{{{(2r - 1)}^2}}} = \frac{{{\pi ^2}}}{8},} $$ then $$\sum\limits_{r = 1}^\infty  {\frac{1}{{{r^2}}}} $$ is equal to 

The sum  $$\frac{3}{{1.2}},\frac{3}{{1.2}},\frac{1}{2},\frac{4}{{2.3}}{\left( {\frac{1}{2}} \right)^2} + \frac{5}{{3.4}}{\left( {\frac{1}{2}} \right)^2}$$

If f(x)= $$x+\frac{1}{2x+\frac{1}{\frac{1}{2x+...\infty }}}$$ ; 

Equation $${x^n} - 1 = 0,n \in N,$$ has roots $$1,{a_2},.....{a_n}$$.
The value of $$\sum\limits_{r = 2}^n {\frac{1}{{1 - {a_r}}},} $$ is

Fill in the missing values.

The number of the three digits numbers having only two consecutive digits identical is:

$$1 + \frac{1}{{1 + 2}} + \frac{1}{{1 + 2 + 3}} + \frac{1}{{1 + 2 + 3 + 4}} + ...... + \frac{1}{{1 + 2 + ... + 2015}}$$

Find the missing number in the given figure?

If $$24 + 37 = 7,12 + 18 = 3$$, then 54+21=?

In the following number series,one number is wrong.find out the ?

1,2,8,33,149,765,4626