print(`The form in 1-1 is WZ`):
print(``):

print(`F:= (-1)^k/(1-q^(k+1))/qbin(n+k+1,k+1)*(q)_n/(q^2)_n`):

print(`G:= (-1)^k/(1-q^(k+1))/qbin(n+k+1,k+1)*(q)_n/(q^2)_n*q^(n+1)/(1+q^(n+1))`):

print(`It suffices to verify that NF - F = KG - G`):
print(``):

print(`or, equivalently:`):
print(`NF/F - 1 -KG/F + G/F = `):
print(``):
gu:=(1-q^(n+1))/(1+q^(n+1))/(1-q^(n+k+2))-1 -(-1)*(1-q^(k+1))/(1-q^(n+k+2))*q^(n+1)/(1+q^(n+1))+q^(n+1)/(1+q^(n+1)):

print(gu, `=`,simplify(gu)):

print(`This took`):
print(time()):
print(`Seconds of CPU time`):