What is the value of following series
1/(7^1) + 2/(7^2) + 1/(7^3) +2/(7^4) + 1/(7^5) +......

• 1/(7^1) + 2/(7^2) + 1/(7^3) +2/(7^4) + 1/(7^5) +......
  can be written as
  
  1/7+1/7^2+1/7^2+1/7^3+1/7^4+1/7^4+1/7^5+......
  =>(1/7+1/7^2+1/7^3+1/7^4+1/7^5+......)+(1/7^2+1/7^4+ 1/7^6+.......)
  Two GP series one with a=1/7 and r=1/7
  second with a=1/7^2 and r= 1/7^2
  
  sum of GP to infinity ( when r is small) = a/1-r
  so sum of expression = (1/7/1-1/7)+(1/7^2/1-1/7^2) =(1/6)+(1/48)= 3/16
• 12 years agoHelpfull: Yes(19) No(0)
• this we can write as 1/7+1/7^2+1/7^2+1/7^3+1/7^4+1/7^4+1/7^5+...... =>(1/7+1/7^2+1/7^3+1/7^4+1/7^5+......)+(1/7^2+1/7^3+.......) by the concept of geometric progression (1/7/1-1/7)+(1/7^2/1-1/7^2) =>(1/6)+(1/48)= 9/48=3/16
• 12 years agoHelpfull: Yes(4) No(1)
• Is it
  
  1/7 + 2/72 + 1/73 +2/74 + 1/75 +
  
  or
  
  1/7 + 2/7^2 + 1/7^3 +2/7^4 + 1/7^5 +
• 12 years agoHelpfull: Yes(1) No(2)
• 3/16
  
  9/(7^2){1+1/(7^2)+...}
• 9 years agoHelpfull: Yes(0) No(1)