1.

Units digit of (1^3+2^3.......10^3)^10

Answer»

Sum of cube of FIRST n NATURAL no. is sqaure of n*(n+1)/2.
hence, expression is {(10*11/2)^2}^10=55^20
by observing, unit place shall be 5.
otherwise
expanding the expession (5+50)^20, we get
C0 5^20+C1*5^19*50++++++++
C0 5^20+multiple of 10

now unit place have same value as that of 5^20 i.e 5


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