Question

Ofer 99 puncte ! Se considera expresia E (x) = 2x + 1 / x ^ 2 ( x + 1 ) ^2. Sa se calculeze : E (1)+E (2)+E(3) +.....+ E (2015)

Answer 1

E(x) = 1 / x²   -  1 / ( x +1) ² 
E(1) = 1 / 1²   -   1 / 2²
E(2) = 1 /2²   -   1 /  3² 
E ( 3) = 1 / 3²  - 1 / 4² 
.....................
E( 2013) = 1 / 2013²  - 1 / 2014²
E( 2014) = 1 /2014²   - 1 / 2015²
E( 2015) = 1 / 2015²  - 1 / 2016² 
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suma = 1  - 1 / 2016² = ( 1 - 1 /2016 ) · ( 1 + 1 /2016) = 2015 · 2017 /2016²