Question

Va rooog ajutor !!!
Calculati
$s = 1( {10}^{2} - {10}^{1} ) + 2( {10}^{3} - {10}^{2}) + ... + 2016( {10}^{2017} - {10}^{2016} + 2017$

Answer 1

s=1(10²-10¹)+2(10³-10²)+...........+2016(10²⁰¹⁷-10²⁰¹⁶)+2017

s=1(10²⁻¹)+2(10³⁻²)+...........+2016(10²⁰¹⁷⁻²⁰¹⁶)+2017

s=1×10+2×10+...........2016×10+2017 =10(1+2+3+...............+2016)+2017

paranteza este suma Gauss

1+2+3+...2016=(2016×2017):2=1013×2017

s=1013×2017+2017=2017(1013+1)=2017×1014=2045238