Question

calculati 1+3+5+7+...+307

Answer 1

1 + 3 + 5 + 7 +...+ 2n-1 = n²

2n - 1 = 307 => 2n = 308 => n = 154

1 + 3 + 5 + 7 +...+ 307 = 154² = 23 716

Answer 2

1 + 3 + 5 +  7 + ... + 307

Este de forma  1 + 3 + 5 +  7 +...+ 2n -  1 = n × n

307 = 2n - 1 de unde 2n = 307 + 1 ⇒ 2n = 308 ⇒n = 308 : 2 ⇒ n = 154

Deci suma S = 154 × 154 = 23716

sau

1 + 3 + 5 +....+307 = 1 + (1 + 2) + (1 + 4) +....+ (1 + 306)

(1 + 1 +... + 1) + 2( 1 + 2 + 3 +...153)

154 + 2× (153×154 ): 2 = 154 + 23562 = 23716

1 + 3 + 5 +  7 + ... + 307  = 23716