Question

[phương]

tính nhanh giúp mk với ạ mk cảm ơn nhiều

Answer 1

[Akai Haruma]

Lời giải:
Gọi tử số là T

\(T=\frac{2-1}{1\times 2}+\frac{4-3}{3\times 4}+\frac{6-5}{5\times 6}+....+\frac{60-59}{59\times 60}\)

\(=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{59}-\frac{1}{60}\)

\(=(1+\frac{1}{3}+\frac{1}{5}+....+\frac{1}{59})-(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{60})\)

\(=(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{59}+\frac{1}{60})-2\times (\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{60})\)

\(=(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{59}+\frac{1}{60})-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{30})\)

\(=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{60}=\text{mẫu số}\)

Do đó $D=1$