Sequences and S...

The value of the product 
$${ 6 }^{ \frac { 1 }{ 2 }  }\times { 6 }^{ \frac { 1 }{ 4 } }\times { 6 }^{ \frac { 1 }{ 8 } }\times { 6 }^{ \frac { 1 }{ 16 }  }\times ..$$ up to infinite terms is

Select the missing number from the given alternatives.

If $$12\times 16 = 188$$ and $$14\times 18 = 248$$, then find the value of $$16\times 20 = ?$$

If a and b are two unequal positive numbers, the:

If $$y = x+x^2+x^3+...$$ up to infinite terms, where $$ x<1$$, then which one of the following is correct?

The value of $$\dfrac { 1 }{ \log _{ 3 }{ e }  } +\dfrac { 1 }{ \log _{ 3 }{ e^2 }  } +\dfrac { 1 }{ \log _{ 3 }{ e^4 }  } +...$$  up to infinite terms is

If $$x =1-y+{ y }^{ 2 }-{ y }^{ 3 }+...$$ upto infinite terms, where |y| < 1, then which one of the following is correct?

If $$1.3 + 2.3^2 + 3.3^3 +...+ n.3^n $$= $$\dfrac { (2n-1)3^ a+b }{ 4 }$$ then $$a$$ and $$b$$ are respectively 

 General term of 4 + 6 + 9 + 13 + 18 + .......to n terms

$$\displaystyle \sum _{ k=1 }^{ 6 }{ \left[ sin\frac { 2k\pi  }{ 7 } -i\quad cos\quad \frac { 2k\pi  }{ 7 }  \right]  } =$$