Given : t_k=k(k!),

Then    =  S_n  =   1.1!  +  2.2!  +  3.3!  + ................. + n.n!

Let : V_n  =  ( n + 1 )!

So: V_{n -1}  =  n!

V_n  -  V_{n -1}   =   (n + 1)!  -  n!   =   n.n!   =   T_n

V_{n -1}  -  V_{n -2}   =   n!  -  (n - 1)!   =   (n - 1).(n - 1)!   =   T_{n -1}

.

.

V₁  -  V₀   =   2!  -  1!   =   1.1!   =   T₁

Therefore:  S_n  =  T₁ + T₂ + T₃ + ......... + T_n

                         =  V_n  -  V₀ 

                         =  (n + 1)!  -  1

True.

The series can be written as:  ( 1  -  1/2 )  +  ( 1/2  -  1/3 )  +  ( 1/3  -  1/4 )  +  ..................  +  ( 1/n  -  1/(n + 1) )

                                                  =   1  -  1/( n + 1 )

When 'n' tends to infinity, the sum of the series upto infinity is equal to : 1 

Imagine yourself sitting in the class on the first day of your college life at IIT........

WHAT is/are the best answer(s) you can give, to these 3 simple questions:

WHY have you decided to take

E.C.

 Mechanical

 Computer Science

Imagine yourself sitting in the class on the first day of your college life at IIT........

WHAT is the best answer you can give to these simple questions:

WHY have you decided to take

E.C.

 Mechanical

 Computer Science

I think the answer for the 1st question is 2

Correspondence Course :

* BRILLIANT TUTORIALS

* NARAYANA

*FIIT JEE

*RESONANCE

*ANY OTHER



WHICH IS THE BEST AMONG THESE???

Correspondence Course :

* BRILLIANT TUTORIALS

* NARAYANA

*FIIT JEE

*RESONANCE

*ANY OTHER





WHICH IS THE BEST AMONG THESE???

Correspondence Course :

* BRILLIANT TUTORIALS

* NARAYANA

*FIIT JEE

*RESONANCE

*ANY OTHER



WHICH IS THE BEST AMONG THESE???

Let 'F' be the first term of the A.P. and 'L' be the last term of the A.P.

Given:

a  =  ( p / 2 )( F + L )

b  =  ( q / 2 )( F + L )

c  =  ( r / 2 )( F + L ) 

Therefore:

( a / p )( q - r )  +  ( b / q )( r - p )  +  ( c / r )( p - q )   =   ( 1 / 2 )( F + L )  [  {q - r} + {r - p} + {p - q}  ]

                                                                                       =   0 

Question 2

If we consider the +ive x - axis, +ive y - axis and +ive z - axis, then  X  X  Y =  Z ie, X  X  Y is along +ive z - axis

Now consider the vector A pointing vertically upwards( along +ive x - axis ) and B pointing north ( along +ive y - axis ), then A X B is along the +ive z - axis, that is, along the west.  

Question 1

Dimensionless quantities may have units. For example : Angle is a dimensionless quantity, but one of its unit is "radian".

Let the G.P. be :       a , ar , ar² , ar³ , ............ ar^{2n - 1}       where 'r' is the common ratio

Given :   S1  =  a + ar² + ar⁴ + ........... + ar^{2n - 2}   =  a( (r² )ⁿ  -  1 ) / r² - 1

               S2  =  ar + ar³ + ar⁵ + ............. + ar^{2n - 1}   =  ar ( (r²)ⁿ  -  1 ) / r² - 1

Therefore : S2 / S1  =  r