Question

[nguyễn văn nam]

tim so tu nhien x , biet :

 a, 1+2+3+...+x = 210

b, 2¹+2³+2⁵+....+2^x=2^{100  -2}

Answer 1

[Nguyễn Phương Uyên]

a, 1 + 2 + 3 + ... + x = 210

=> (1 + x)x : 2 = 210

=> x(x + 1) = 420

=> x(x + 1) = 20.21

=> x = 20

vậy_

b, 2¹ + 2² + 2³ + ... + 2^x = 2¹⁰⁰ - 2

đặt A = 2¹ + 2² + 2³ + ... + 2^x 

=> 2A = 2² + 2³ + 2⁴ + ... + 2^{x + 1}

=> 2A - A = (2² + 2³ + 2⁴ + ... + 2^{x + 1}) - (2¹ + 2² + 2³ + ... + 2^x)

=> A = 2^{x + 1} - 2

=> 2^{x + 1} - 2 = 2¹⁰⁰ - 2

=> x + 1 = 100

=> x = 99