Q. Last Digit of the Summation of Series
1^4+2^4+3^4+4^4+...........S90^4

• The last digit of any number raised to power 4 is either 1,6,5,0
  In the given series if you will find the power of the number you will get series of unit digits as:
  
  1^4 : unit digit = 1
  2^4 : unit digit = 6
  3^4 : unit digit = 1 ...
  
  over all series of unit digits will be like this
  
  1,6,1,6,5,6,1,6,1,0 (1 - 10)
  1,6,1,6,5,6,1,6,1,0 (11 - 20)
  ...
  same for 21-30, 31-40, ....., 81-90
  
  adding the unit digits we get sum = 33 * 9 = 297
  
  so unit digit = 7
• 10 years agoHelpfull: Yes(15) No(3)
• for the fourth power the formula is [n(n+1)(3n^2+2n+1)]/30... thushere we have 90 terms from 1 to 90 therefore [90(90+1)(3*8100+2*90+1)]/30 = 6707883 thus last digit is 3
• 10 years agoHelpfull: Yes(0) No(1)