Question

1) Tính tổng A = 2¹⁰ + 2¹¹ + 2¹² + 2¹³ + ... + 2²⁰¹⁵

2) Tìm số nguyên x, y thỏa mãn : ( 2x + 1 ) ( y - 7 ) = 2014

Answer 1

1) A=2¹⁰+2¹¹+2¹²+2¹³+......+2²⁰¹⁵

2A=2(2¹⁰+2¹¹+2¹²+.......+2²⁰¹⁵)

2A=2¹¹+2¹²+2¹³+........+2²⁰¹⁵+2²⁰¹⁶

2A-A=2²⁰¹⁶-2¹⁰

A=2²⁰¹⁶-2¹⁰

Vậy: A=2²⁰¹⁶-2¹⁰

Answer 2

2: 

(2x+1)(y-7)=2014

=>\(\left(2x+1;y-7\right)\in\left\{\left(1;2014\right);\left(-1;-2014\right);\left(19;106\right);\left(-19;-106\right);\left(53;38\right);\left(-53;-38\right);\left(1007;2\right);\left(-1007;-2\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(0;2021\right);\left(-1;-2017\right);\left(9;113\right);\left(-10;-99\right);\left(26;45\right);\left(-27;-31\right);\left(503;9\right);\left(-504;5\right)\right\}\)