Sum of series

[shobby]

Find the sum of the series 1(2) + 2(2^2) + 3(2^3) + ... + 100(2^100).

a) 100(2^101) + 2

b) 99(2^100) + 2

c) 99(2^101) + 2

d) 100(2^100) + 2

 

How to proceed with such questions?

 

 

OA - C

 

 

[Queen09]

S= 1(2) + 2(2^2) + 3(2^3) + ... ..........+ 100(2^100)

2*S= 1(2^2) + 2(2^3) + 3 (2^4) + ...................+ 100 (2^101)

 

In 2*S and S match and subtract the terms with same values of 2^n

 

we get, 2*S - S = last term of 2*s - first term of S - [g.p of 2^2 + 2^3 ....2^100]

=> 100 (2^101) - 1 (2) - [2^2 + 2 ^ 3 + ......2^100]

 

S = 100 (2^101) - 2 (2^100 -1)

S = 100 (2^101) - 2^101 + 2

=> S= 99(2^101) + 2

[e.cartman]

Oh, I had completely forgotten that neat little strategy which we often used as students. Thanks Queen09!

[getsetgo]

This is arthimeticogemetric series...There is a straight formula to solve this..unfortunately I dont remember the formula,so I proceed as..

 

a=1(2) + 2(2^2) + 3(2^3) + ... + 100(2^100)..........eqn1

2a= 1.2^2 + 2(2^3)+.....+ 99(2^100) + 100.2^101....eqn2

Subtracting eqn2 from eqn1

-a=1(2)+1.2^2+1.2^3+............+ 1.2^100 - 100.2^101

-a=-99.2^101-2

a=99.2^101+2....C

[shobby]

S= 1(2) + 2(2^2) + 3(2^3) + ... ..........+ 100(2^100)

2*S= 1(2^2) + 2(2^3) + 3 (2^4) + ...................+ 100 (2^101)

 

In 2*S and S match and subtract the terms with same values of 2^n

 

we get, 2*S - S = last term of 2*s - first term of S - [g.p of 2^2 + 2^3 ....2^100]

=> 100 (2^101) - 1 (2) - [2^2 + 2 ^ 3 + ......2^100]

 

S = 100 (2^101) - 2 (2^100 -1)

S = 100 (2^101) - 2^101 + 2

=> S= 99(2^101) + 2

 

[clap] Thanks!

[genius_in_the_gene]

S= 1(2) + 2(2^2) + 3(2^3) + ... ..........+ 100(2^100)

2*S= 1(2^2) + 2(2^3) + 3 (2^4) + ...................+ 100 (2^101)

 

In 2*S and S match and subtract the terms with same values of 2^n

 

we get, 2*S - S = last term of 2*s - first term of S - [g.p of 2^2 + 2^3 ....2^100]

=> 100 (2^101) - 1 (2) - [2^2 + 2 ^ 3 + ......2^100]

 

S = 100 (2^101) - 2 (2^100 -1)

S = 100 (2^101) - 2^101 + 2

=> S= 99(2^101) + 2

 

Cool:tup:.

But this seems more like a CAT question than a GMAT one

[rite237]

why do we need to solve this? this is not part of GMAT syllabus