Suppose we want to prove the statement S(n): "If n ⥠2, the sum of the integers 2 through n is (n+2)(n-1)/2" by induction on n. To prove the inductive step, we can make use of the fact that 2+3+4+...+(n+1) = (2+3+4+...+n) + (n+1) Find, in the list below an equality that we may prove to conclude the inductive part. a. If n ⥠3 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
b. If n ⥠1 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
c. If n ⥠2 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
d. If n ⥠1 then (n+2)(n-1)/2 + n + 1 = n(n+3)/2

The instruction ishl (shift left integer) exists in jvm but not in ijvm. it uses the top two values on the stack, replacing the two with a single value, the result. the sec- ond-from-top word of the stack is the operand to be shifted. its content is shifted left by a value between 0 and 31, inclusive, depending on the value of the 5 least signifi- cant bits of the top word on the stack (the other 27 bits of the top word are ignored). zeros are shifted in from the right for as many bits as the shift count. the opcode for ishl is 120 (0x78).a. what is the arithmetic operation equivalent to shifting left with a count of 2? b. extend the microcode to include this instruction as a part of ijv.

Which excel file extension stores automated steps for repetitive tasks?

Fall protection, confined space entry procedures, controlled noise levels, and protection from chemical hazards are some of the things that contribute to a safe and