Question

[quỳnh nguyễn]

4/1.3 + 4/3.5 + 4/5.7 +...+ 4/ 97.99

Answer 1

[Sahara]

\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{3}{5.7}+...+\dfrac{4}{97.99}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\left(1-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{98}{99}\)
\(=\dfrac{196}{99}\)
#NoSimp

Answer 2

[Nguyễn Lê Phước Thịnh]

=2(2/1*3+2/3*5+...+2/97*99)

=2(1-1/3+1/3-1/5+...+1/97-1/99)

=2*98/99=196/99