Latest Elitmus Aptitude Question SOLUTION: Q. Last Digit of the Summation of Series 1^4+2^4+3^4+4^4+...........S90^4

• Placement Papers
• /
• Elitmus

Elitmus Question Papers:

(#M40030997) ELITMUS question Quant Keep an EYE

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

Asked In Elitmus Abhishek Singh (10 years ago)

Unsolved Read Solution (2)

Is this Puzzle helpful?   (0)   (0) Submit Your Solution

Read Solution (2) :

Ankit Goyal  (10 years ago)

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

Is this solution Helpfull? Yes (15) | No (3)  

Priyansh   (10 years ago)

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

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.