Question

1+2+4+8+16+....+4096+8192

Answer 1

= 1 + 2 + 2² + 2³  + ..... + 2¹² + 2¹³

= 2(1 + 2 + 2² + 2³  + ..... + 2¹² + 2¹³) - (1 + 2² + 2³ + 2⁴ + ..... + 2¹² + 2¹³)

= 2 + 2² + 2³ + 2⁴ + .... + 2¹³ + 2¹⁴ - 1 - 2² - 2³ - 2⁴ - ..... - 2¹² - 2¹³

= 2¹⁴ - 1

= 16383

Answer 2

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