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Last Digit (Posted on 2004-01-23) Difficulty: 3 of 5
Find the last digit of summation of the series:
(1)^99 + (2)^99 + (3)^99 + (4)^99 + + (98)^99 + (99)^99

  Submitted by Ravi Raja    
Rating: 2.4000 (5 votes)
Solution: (Hide)
We group the sum as follow:
[(1)^99 + (11)^99 + ... + (91)^99] + [(2)^99 + (22)^99 + ... (92)^99] + ...... + [(9)^99 + (19)^99 + ... + (99)^99] + [(10)^99 + (20)^99 + (30)^99 + ... (90)^99]
All the terms in a single group have the same last digit (i.e. last digits of 199 + 1199 + ... + 9199 are same, is 1, & similarly for the other groups).
Also, there are 10 terms in each group except for the last one. Therefore the last digit of the sum of terms in first 9 groups is 0. (as whatever be the last digit, we have to multiply it by 10) And the last digit of the sum of the terms in the group 10 is obviously 0.
Hence, the last digit of the series is 0.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionsolutionPraneeth Yalavarthi2007-07-09 08:41:41
Some Thoughtsre(2): last digitAdy TZIDON2004-01-31 13:23:30
Some Thoughtsre(2): Last two digitsNick Hobson2004-01-31 07:57:31
re: Last two digitsRichard2004-01-30 22:09:15
SolutionLast two digitsNick Hobson2004-01-30 15:22:31
Some Thoughtsre: last digite.g.2004-01-27 09:16:50
Solutionlast digitPurna2004-01-24 05:08:27
No SubjectPurna2004-01-24 05:04:45
No SubjectPurna2004-01-24 05:04:34
re(4): solutionAdy TZIDON2004-01-23 10:41:49
re(3): solutionCharlie2004-01-23 10:38:36
Some Thoughtsre(3): solution --- Gosh!!!..Ady TZIDON2004-01-23 10:38:04
re(2): solutionSilverKnight2004-01-23 10:36:32
re(2): solution --- Gosh!!!..Charlie2004-01-23 10:22:38
re(2): solutionAdy TZIDON2004-01-23 10:21:36
re: solutionCharlie2004-01-23 10:07:55
Some Thoughtsre: solutionAdy TZIDON2004-01-23 10:03:35
SOLUTIONAdy TZIDON2004-01-23 09:57:59
SolutionsolutionSilverKnight2004-01-23 09:47:03
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