Question

Daca a)1/2+2/3+3/4+4/5+5/6 si b)1/2+1/3/1/4+1/5/1/6 afla a+2017+b

Answer 1

$a+2017+b = \\ \\= \sum\limits_{k=1}^6 \Big( \dfrac{k-1}{k}\Big) +2017 + \sum\limits_{k=1}^6 \Big(\dfrac{1}{k}\Big) = \\ \\ \sum\limits_{k=1}^6 \Big( \dfrac{k-1}{k}\Big) + \sum\limits_{k=1}^6 \Big(\dfrac{1}{k}\Big) +2017 = \\ \\ = \sum\limits_{k=1}^6 \Big( \dfrac{k-1}{k}+ \dfrac{1}{k}\Big) + 2017 = \\ \\ = \sum\limits_{k=1}^6 \Big( \dfrac{k}{k}-\dfrac{1}{k} + \dfrac{1}{k}\Big) + 2017 = \\ \\ = \sum\limits_{k=1}^6 (1)+ 2017 = \\ \\ = 6+2017 = \\ \\= 2023$

Answer 2

a=1/2+2/3+3/4+4/5+5/6 ;             b=1/2+1/3/1/4+1/5+1/6

a+b=1/2+2/3+3/4+4/5+5/6 +1/2+1/3/1/4+1/5+1/6
a+b=(1/2+1/2)+(2/3+1/3)+(3/4+1/4)+(4/5+1/5)+(5/6+1/6)
a+b=2/2+3/3+4/4+5/5+6/6
a+b+2017=5+2017
a+b+2017=2022