Question

2(1+3+3la puterea2+.…+3la puterea50)mai mic decât 3la puterea50




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Answer 1

S = 1 + 3 + 3² + .. + 3⁵⁰

3S = 3 + 3² + .. + 3⁵¹

Adunam, scadem 1

3S = (1 + 3 + 3² + .. + 3⁵⁰) + 3⁵¹ - 1

In paranteza avem S

3S = S + 3⁵¹ - 1

scadem S

2S = 3⁵¹ - 1

3⁵¹ - 1 > 3⁵⁰