Question

Va rog!! imi poate explica cineva cum pot face aceste sume gauss??am olimpiada maine

Answer 1

[tex]S=\dfrac{1}{2\cdot 3}+\dfrac{1}{3\cdot 4}+\ldots+ \dfrac{1}{2015\cdot 2016}\\ S=\dfrac{3-2}{2\cdot 3}+\dfrac{4-3}{3\cdot 4}+\ldots+\dfrac{2016-2015}{2015\cdot 2016}\\ S=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\ldots+\dfrac{1}{2015}-\dfrac{1}{2016}\\ S=\dfrac{1}{2}-\dfrac{1}{2016}=\dfrac{1007}{2016}\\ \text{La T nu prea ai ce sa ii faci.Eventual:}\\ T=\dfrac{6+1}{6}+\dfrac{12+1}{12}+\ldots+\dfrac{4062240+1}{4062240}\\ [/tex]

[tex]T=\underbrace{1+1+\ldots+1}+\dfrac{1}{6}+\dfrac{1}{12}+\ldots+\dfrac{1}{4062240}\\ ~~~~~~~~~de\ 2014\ ori\\ T=2014+\text{suma de fractii}[/tex]