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

• ------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
  
• 10 years agoHelpfull: Yes(22) No(4)
• 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
• 10 years agoHelpfull: Yes(4) No(0)
• But the options were
  a. 99(2)^100+2
  b. 100(2)^100+2
  c. 101(2)^100+2
  d. 101(2)^101+2
• 10 years agoHelpfull: Yes(3) No(1)
• 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)
• 10 years agoHelpfull: Yes(1) No(2)
• this solutions are so confusing can any one explain this concept by taking a simple example....
• 10 years agoHelpfull: Yes(1) No(0)
• pls explain it didnt get it
• 10 years agoHelpfull: Yes(0) No(0)
• 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.
• 10 years agoHelpfull: Yes(0) No(0)
• can you plzz give clear solution off.. it.. i didnt get it rakesh cn u explain it
• 10 years agoHelpfull: Yes(0) No(0)