1708Is it = 6
1) Find the last digit of ((5!+9)(6!+4))100!
How do we do these types of sums? i think we can't do this by taking modulo 10...
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5 Answers
1057it shud be 6...
(5!+9)(6!+4) has 6 in its units place since 5! and 6! end in zeroes and 9 x 4 = 36
and we know 6 to the power any positive integer we get 6 only in the units digit....
1057sigma for dese type of sums...
u shud know de cyclicity of digits....
for example 2...
21=2
22=4
23=8
24-16
25=32
we see that the units digit repeat in the pattern 2,4,6,8,2,4,6,8 with a period of 4...
all digits have dis cyclicity
cyclicity of 3 is 4(3,9,7,1)
cyclicity of 4 is 2(4,6)
cyclicity of 5 is 1(only 5)
and so on.....
3well every such number has to have a cycle of the last digits.
the cycle can be of max period 4.
this is for the last digit only.
for the tens digit and all, the cycle has a larger period, though their are numbers with small periods of their tens digits too like 7...
it is so cause n^5 - n is always divisible by 10 ...