Latest TCS Aptitude Question SOLUTION: 1(2)+2(2)^2+3(2)^3+.......+100(2)^100

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(#M40032293) TCS Numerical Ability question Sum Keep an EYE

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

Asked In TCS kumar sudheer (10 years ago)

Solved RAKESH Read Solution (8)

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Read Solution (8) :

RAKESH  (10 years ago)

------correction for previous answer------
S=1(2)+2(2)^2+3(2)^3+.......+100(2)^100
(-)2*S= 1(2)^2+2(2)^3+.......+99(2)^100+100(2)^101
-------------------------------------------------------
=>S-2S=2+2^2+2^3+2^4+.........+2^100-100*2^101
=> -S=2(2^100-1)/(2-1)-100*2^101
=> S=100*2^101-2(2^100-1)
=> S=100*2^101-2^101+2
=> S=99*2^101+2

Is this solution Helpfull? Yes (22) | No (4)  

aditi bose  (10 years ago)

s=1(2)+2(2)^2+3(2)^3+......+100(2)^100
2s= 1(2)^2 + 2(2)^3 + 3(2)^4 + .....+ 99(2)^100 + 100(2)^101
s-2s = [1(2) + 1(2)^2 + 1(2)^3 + ....+ 1(2)^100 ]- 100(2)^101
-s= 2(2^100 -1 / 2-1 ) - 100(2)^101
-s= 2^101 - 2 - 100(2)^101
s= -2^101 + 2 + 100(2)^101
s= (100-1)2^101 +2
s= 99(2)^101 +2

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kumar sudheer  (10 years ago)

But the options were
a. 99(2)^100+2
b. 100(2)^100+2
c. 101(2)^100+2
d. 101(2)^101+2

Is this solution Helpfull? Yes (3) | No (1)  

RAKESH  (10 years ago)

S=1(2)+2(2)^2+3(2)^3+.......+100(2)^100
(-)2*S= 1(2)^2+2(2)^3+.......+99(2)^100+100(2)^101
---------------------------------------------------
S-2S=2+2^2+2^3+2^4+.........+2^100-100*2^101
=> -S=2(2^100-1)/(100-1)-100*2^101
=> S=100*2^101-(2/99)(2^100-1)

Is this solution Helpfull? Yes (1) | No (2)  

hemant panchal  (10 years ago)

this solutions are so confusing can any one explain this concept by taking a simple example....

Is this solution Helpfull? Yes (1) | No   

sana farheen  (10 years ago)

pls explain it didnt get it

Is this solution Helpfull? Yes | No   

SAYANTAN SAHA  (10 years ago)

If the options are-
a. 99(2)^100+2
b. 100(2)^100+2
c. 101(2)^100+2
d. 101(2)^101+2

Then it is a dummy question. Dont answer this questions.

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preeti jijnodiya  (9 years ago)

can you plzz give clear solution off.. it.. i didnt get it rakesh cn u explain it

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