Pre Calc
posted by Lauren on .
Solve for A and B if:
1 A B
 =  + 
k(k+1) k k+1

the 1 is over k(k+1), and the A is over k, and the B is over k+1

common denominator: k(k+1)
1/[(k)(k+1)]=A(k+1)/[(k)(k+1)] + B(k)/[(k)(k+1)]
1/[(k)(k+1)]= [ A(k+1)+ B(k)]/ [(k)(k+1)]
cross multiply:
[(k)(k+1)]= [ A(k+1)+ B(k)][(k)(k+1)]
cancel like terms:
1= [ A(k+1)+ B(k)]
solve for k!