What are the last 2 digits of the sum 1 + 11 + 111 + ... + 111...111 (last one has 50 digits)?
This is a question from Junior Math Olympiad.
Question : What are the last 2 digits of the sum 1 + 11 + 111 + ... + 111...111 (last one has 50 digits)?
Solution: Here is tiny python program. Also available http://www.codeskulptor.org/#user43_XiVvNuzfshT3lKX.py
# What are the last 2 digits of the sum
# 1 + 11 + 111 + ... + 111...111 (last one has 50 digits?
total_num = 50
this_num = 0
sum = 0
for i in range(total_num):
this_num = 10 ** i + this_num
print "Number " + str(i+1) +":", this_num
sum = sum + this_num
print "Total Sum:", sum
Output:
Answer:
Last 2 digit will be - 40
Question : What are the last 2 digits of the sum 1 + 11 + 111 + ... + 111...111 (last one has 50 digits)?
Solution: Here is tiny python program. Also available http://www.codeskulptor.org/#user43_XiVvNuzfshT3lKX.py
# What are the last 2 digits of the sum
# 1 + 11 + 111 + ... + 111...111 (last one has 50 digits?
total_num = 50
this_num = 0
sum = 0
for i in range(total_num):
this_num = 10 ** i + this_num
print "Number " + str(i+1) +":", this_num
sum = sum + this_num
print "Total Sum:", sum
Output:
Number 1: 1 Number 2: 11 Number 3: 111 Number 4: 1111 Number 5: 11111 Number 6: 111111 Number 7: 1111111 Number 8: 11111111 Number 9: 111111111 Number 10: 1111111111 Number 11: 11111111111 Number 12: 111111111111 Number 13: 1111111111111 Number 14: 11111111111111 Number 15: 111111111111111 Number 16: 1111111111111111 Number 17: 11111111111111111 Number 18: 111111111111111111 Number 19: 1111111111111111111 Number 20: 11111111111111111111 Number 21: 111111111111111111111 Number 22: 1111111111111111111111 Number 23: 11111111111111111111111 Number 24: 111111111111111111111111 Number 25: 1111111111111111111111111 Number 26: 11111111111111111111111111 Number 27: 111111111111111111111111111 Number 28: 1111111111111111111111111111 Number 29: 11111111111111111111111111111 Number 30: 111111111111111111111111111111 Number 31: 1111111111111111111111111111111 Number 32: 11111111111111111111111111111111 Number 33: 111111111111111111111111111111111 Number 34: 1111111111111111111111111111111111 Number 35: 11111111111111111111111111111111111 Number 36: 111111111111111111111111111111111111 Number 37: 1111111111111111111111111111111111111 Number 38: 11111111111111111111111111111111111111 Number 39: 111111111111111111111111111111111111111 Number 40: 1111111111111111111111111111111111111111 Number 41: 11111111111111111111111111111111111111111 Number 42: 111111111111111111111111111111111111111111 Number 43: 1111111111111111111111111111111111111111111 Number 44: 11111111111111111111111111111111111111111111 Number 45: 111111111111111111111111111111111111111111111 Number 46: 1111111111111111111111111111111111111111111111 Number 47: 11111111111111111111111111111111111111111111111 Number 48: 111111111111111111111111111111111111111111111111 Number 49: 1111111111111111111111111111111111111111111111111 Number 50: 11111111111111111111111111111111111111111111111111 Total Sum: 12345679012345679012345679012345679012345679012340
Answer:
Last 2 digit will be - 40
Why the sum is 40?
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