find the units digit of expression 11^1+12^2+13^3+14^4+15^5+16^6

Question

anonymous · Answer

11^1+12^2+13^3+14^4+15^5+16^6=17577359
9

mathmath333 · Answer

do i have to calculate whole thing

anonymous · Answer

Probably not.  I use Mathematica v9 Home Edition for calculations on this site.
The problem expansion and sum took 19 micro seconds on a mid 2010 IMAC.

mathmath333 · Answer

ok

mathmath333 · Answer

where do i get Mathematica v9 Home Edition

anonymous · Answer

Look at the units digits
{ 1^1, 2^2, 3^3, 4^4,   5^5,     6^6 }
{ 1,         4,    27, 256,  3125, 46656}
 1+4+7+6+5+6 = 29
9

anonymous · Answer

http://www.wolfram.com/mathematica/new-in-10/?src=google&416&gclid=CMCV0__QmcACFUEbaQodXoQA9w Mathematica v10 just released. Mine is v9. Special rate for students or at least there was.