Latest Elitmus Aptitude Question SOLUTION: 1^4+2^4+3^4+............n^4 if n=90 then S90=???? what will be the last digit..of the series

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

Asked In Elitmus azad yadav (9 years ago)

Unsolved Read Solution (9)

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naidu  (9 years ago)

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.

Is this solution Helpfull? Yes (39) | No   

soudipta  (9 years ago)

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

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Tapas   (9 years ago)

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..

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naidu  (9 years ago)

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

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prasanthi  (9 years ago)

last digit is 0

Is this solution Helpfull? Yes (1) | No (6)  

sarojani  (9 years ago)

I think its in the form of AP so last degit is 3

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Santanu Sarkar  (9 years ago)

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

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LAKHAN SINGH  (9 years ago)

8 correct

Is this solution Helpfull? Yes | No (2)  

padam  (9 years ago)

9(1+6+1+6+5+6+1+8+9) solve it last digit is 7

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