Sequences and S...

Find the sum of first $$15$$ terms of the sequence whose $${n}^{th}$$ term is $$3+4n$$.

Let $$\sum _{ r=1 }^{ n }{ { r }^{ 4 } } =f\left( n \right) ,$$ then $$\sum _{ r=1 }^{ n }{ { \left( 2r-1 \right)  }^{ 4 } } $$ is equal to

solve

$$\displaystyle\sum _{ r=1 }^{ n }{ \frac { r }{ { r }^{ 4 }+{ r }^{ 2 }+1 }  } $$ is equal to 

$$C_1 + 2C_2 + 3C_3 + ...... + nC_n$$ is equal to

If in a series $$t_n=\dfrac{n+1}{(n+2)!}$$ then $$\displaystyle\sum^{10}_{n=0}t_n$$ is equal to?

insert the missing number:  5,8,12,17,23,___,38 

There is a certain relationship between the pair of figure on either side of ::. Identify the relationship on the left side and find the missing figure.

Rahul told Anand, "Yesterday I defeated the only brother of the daughter of my grandmother." Whom did Rahul defeat ?

Which number replaces the question mark ?