Question 4
Evaluate the following expressions.
(a) $74\times15-15\times\frac{55}{4}+44\times15-15\times\frac{17}{4}$.
(b) $\frac{2+4+6+8+\cdots+200}{3+6+9+12+\cdots+300}$.
(c) $\frac1{1\times2}+\frac1{2\times3}+\frac1{3\times4}+\cdots+\frac1{2020\times2021}$.
(d) $\frac16+\frac1{12}+\frac1{20}+\frac1{30}+\cdots+\frac1{2070}$.
(e) $\frac1{1\times3}+\frac1{3\times5}+\frac1{5\times7}+\cdots+\frac1{2019\times2021}$.
(f) $1+\frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\cdots+\frac1{1+2+3+\cdots+2020}$.
Answer entry: six simplified values in a;b;c;d;e;f order, using a/b for fractions and semicolons between values.
**Editorial input note:** Use no spaces before or after semicolons.
(a) $74\times15-15\times\frac{55}{4}+44\times15-15\times\frac{17}{4}$.
(b) $\frac{2+4+6+8+\cdots+200}{3+6+9+12+\cdots+300}$.
(c) $\frac1{1\times2}+\frac1{2\times3}+\frac1{3\times4}+\cdots+\frac1{2020\times2021}$.
(d) $\frac16+\frac1{12}+\frac1{20}+\frac1{30}+\cdots+\frac1{2070}$.
(e) $\frac1{1\times3}+\frac1{3\times5}+\frac1{5\times7}+\cdots+\frac1{2019\times2021}$.
(f) $1+\frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\cdots+\frac1{1+2+3+\cdots+2020}$.
Answer entry: six simplified values in a;b;c;d;e;f order, using a/b for fractions and semicolons between values.
**Editorial input note:** Use no spaces before or after semicolons.