Calculate the sum of the series

5 + 55 + 555 + ……..+ n

a) (10n – 1) – (5/9)n b) 50/81(10n – 1) – (5/9)n c) 50/81(10n – 1) – (5/9) d) (10n – 1) – (5/9)5n

• 5+55+555+.............+n fives
  5(1+11+111+1111+.............+n ones)
  5/9(9+99+999+............+n nines)
  5/9(10-1+100-1+1000-1+..............+10^n-1)
  5/9((10+10^2+10^3+........+10^n)-n)
  Geometric progression formula:-a(r^n-1/r-1)
  5/9((10(10^n-1/10-1))-n)
  50/81(10^n - 1)-(5/9)n
• 9 years agoHelpfull: Yes(44) No(1)
• 5+55+555+5555+⋯+55…5n fives
  =5/9(1*9+11*9+111*9.....
  =5/9(9+99+999+9999+⋯+99…9
  =5/9(10−1+10^2−1+10^3−1+⋯+10^n−1)
  =5/9(10^1+10^2+10^3+⋯+10^n−n)
  =5/9((10^n+1−10)/9)−n).
• 9 years agoHelpfull: Yes(15) No(0)
• 5+55+555+5555+⋯+55…5n fives
  =59(9+99+999+9999+⋯+99…9n nines)
  =59(10−1+102−1+103−1+⋯+10n−1)
  =59(101+102+103+⋯+10n−n)
  =59(10n+1−109−n).
• 9 years agoHelpfull: Yes(2) No(14)
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• 9 years agoHelpfull: Yes(1) No(2)