1^4+2^4+3^4+............n^4 if n=90 then S90=???? what will be the last digit..of the series

• Answer would be 9, in qtn they asked about unit digit of Sm
  units digits of 1^4 is 1,2^4 is 6,3^4 is 1,4^4 is 6, 5^4 is 5, 6^4 is 6,7^4 is 1, 8^4 is 6, 9^4 is 1, 10^4 is always 0
  so up to 90 each unit digit repeats 9 times
  Hence unit digit in Sm is 9(1+6+1+6+5+6+1+6+1) =9(33) ......results unit digit 7.
  
• 9 years agoHelpfull: Yes(39) No(0)
• 1 + 16 + 81 + 256 + .. + n^4 =(1/5)n^5 + (1/2)n^4 + (1/3)n^3 - (1/30)n
  This last digits of this part [(1/5)n^5 + (1/2)n^4 + (1/3)n^3] will always be zero...as n=90 and the second part will be [90/30]=3
  so now we can think in this way.... 1000-3 = 997 and 100-3= 97 and 10-3 = 7
  Therefore, the last digit will be 7 .....7 is our answer...This is method 1
  Now the second method is
  1^4+2^4+3^4+............9^4 = 1+6+1+6+5+6+1+6+1 = 33 [considering only the last digits]...10^4=0
  11^4+12^4+13^4+............19^4 =33 [considering only the last digits]
  That means [1to 10] + [11to 20] + [21 to 30] +[31 to 40]+[ 41 to 50]+ [51 to 60] + [61 to 70]+ [71 to 80]+ [81 to 90] meaning 9 such series making 1to 90
  Hence 33*9 =297 Last digit is 7 and that is our answer
• 9 years agoHelpfull: Yes(14) No(0)
• unit digits
  1^4=1
  2^4=6
  .....like this for 3=1
  4=6
  5=5
  6=6
  7=1
  8=6
  9=1
  total 33
  so 33*9=unit digit will be 7..
• 9 years agoHelpfull: Yes(6) No(0)
• Answer would be 7, in qtn they asked about unit digit of Sm
  units digits of 1^4 is 1,2^4 is 6,3^4 is 1,4^4 is 6, 5^4 is 5, 6^4 is 6,7^4 is 1, 8^4 is 6, 9^4 is 1, 10^4 is always 0
  so up to 90 each unit digit repeats 9 times
  Hence unit digit in Sm is 9(1+6+1+6+5+6+1+6+1) =9(33) ......results unit digit 7.
  
  Read more at http://www.m4maths.com/80476-placement-puzzle-ans-notification.html#3E6icvg5Vpj1L8g1.99
• 9 years agoHelpfull: Yes(3) No(0)
• last digit is 0
• 9 years agoHelpfull: Yes(1) No(6)
• I think its in the form of AP so last degit is 3
• 9 years agoHelpfull: Yes(0) No(4)
• Considering the last digits we have
  1^4=1,2^4=6,3^4=1.... uptill 9 and then adding all these we get 32
  This is nos. for 1-10 similarly .
  so to get till 90 32*9=288
  the ans is 8
• 9 years agoHelpfull: Yes(0) No(4)
• 8 correct
  
• 9 years agoHelpfull: Yes(0) No(2)
• 9(1+6+1+6+5+6+1+8+9) solve it last digit is 7
• 9 years agoHelpfull: Yes(0) No(0)