Calculate:  $$\left(1+\frac 12+\frac 13+\cdots +\frac 1{149}\right)\times \left(\frac 12+\frac 13+\cdots +\frac 1{149}+\frac 1{150}\right)$$$$-\left(1+\frac 12+\frac 13+\cdots +\frac 1{149}+\frac 1{150}\right)\times \left(\frac 12+\frac 13+\cdots +\frac 1{149}\right)=$$~\uline{~~~~~~~~~~}~. 
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Suppose $$\left(\frac 12+\frac 13+\cdots +\frac 1{149}\right)$$ as $$A$$, $$\left(\frac 12+\frac 13+\cdots +\frac 1{150}\right)$$ as $$B$$.  $$(1+A)\times B-(1+B)\times A=B+AB-A-AB=B-A=\frac 1{150}$$. 