23. b) folosind rezultatul de la punctul a), calculați:
1/2-(1/2^2+1/2^3+1/2^4+...+1/2^10)=..​

Răspuns:

Explicație pas cu pas:

1/2^2 = 1/2 - 1/2^2

1/2^3 = 1/2^2 - 1/2^3

1/2^4 = 1/2^3 - 1/2^4

.......

1/2^10 = 1/2^9 - 1/2^10

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1/2^2 + 1/2^3 + 1/2^4 + ...+ 1/2^10 = 1/2 - 1/2^2 + 1/2^2 - 1/2^3 + 1/2^3 - 1/2^4

+ 1/2^9 - 1/2^10 = 1/2 - 1/2^10

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1/2 - (1/2 - 1/2^10) = 1/2 - 1/2 + 1/2^10 = 1/2^10