What is wrong with this "proof"? "Theorem" For every positive integer n, n i =1 i = (n + 1 2 ) 2 /2. Basis Step: The formula is true for n = 1. Inductive Step: Suppose thatn i=1 i = (n + 1 2 ) 2 /2. Then n+1 i=1 i = ( n i=1 i) + (n + 1). By the induc-tive hypothesis, n+1 i=1 i = (n + 1 2 ) 2 /2 + n + 1 = (n 2 + n + 1 4 )/2 + n + 1 = (n 2 + 3n + 9 4 )/2 = (n + 3 2 ) 2 /2 =[ (n + 1) + 1 2 ] 2 /2, completing the induc-tive step.

The basis step is not even true.

Step-by-step explanation:

The basis step would be for     n = 1.

If the basis step was true then you would have that.

Now. When you say

That's just a fancy way of writing    1.  

On the other hand    

Therefore  

And the basis hypothesis is false.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2