Question

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

Answer 1

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

Answer 2

do i have to calculate whole thing

Answer 3

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.

Answer 4

ok

Answer 5

where do i get Mathematica v9 Home Edition

Answer 6

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

Answer 7

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.