$$1+2+\cdots +2^{20}=2^{21}-1$$  $$1+2+\cdots +2^{6} = 2^{7}-1$$  Subtracting the two equations we have:  $$2^{7}+2^{8}+\cdots +2^{20} = 2^{21}-2^{7}$$ 
Evaluate the following expression:  $$2^{7}+2^{8}+\cdots +2^{19}+2^{20}$$ 
Options:
1: $$2^{20}-2^{6}$$ 
2: $$2^{20}-2^{7}$$ 
3: $$2^{21}-2^{6}$$ 
4: $$2^{21}-2^{7}$$ 
5: None of the above 