If the sum of infinity of the series 1 + 4x + 7x2 + 10x3 - ... is 35/16 then find x.

1) 1/5
2) 2/5
3) 4/5
4) 3/5

• 1/5
  
  S= 1+ 4x + 7x^2 + 10x^3...........(1)
  x*S= x + 4x^2 + 7x^3 + 10x^4......(2)
  subtracting (2) from (1)
  S-x*S = 1+ 3x + 3x^2 + 3x^3....
  
  S*(1-x) = 1+3*(x+x^2+x^3)...
  
  Now x < 1
  
  S*(1-x) = 1+ 3 *(x/(1-x))
  
  Now S=35/16
  
  solving the equation, we get
  x=1/5
• 11 years agoHelpfull: Yes(0) No(0)