Question

cred ca se aplica suma lui Gauss​

Answer 1

= (- 1/2)¹⁺²⁺⁺¹⁰⁰ ₓ (- 1/2) ⁻⁵⁰⁵⁰

= (- 1/2)⁵⁰ˣ¹⁰¹ ₓ (- 1/2) ⁻⁵⁰⁵⁰

= (- 1/2)⁵⁰⁵⁰ ₓ (- 1/2) ⁻⁵⁰⁵⁰

= (- 1/2)⁰

= 1

Answer 2

Explicație pas cu pas:

$(( - \dfrac{1}{2} ) \cdot {( - \dfrac{1}{2} )}^{2} \cdot {( - \dfrac{1}{2} )}^{3} \cdot ... \cdot {( - \dfrac{1}{2}) }^{100} ) \cdot {( - \dfrac{1}{2}) }^{ - 5050} = \\ \\ \\ {( - \dfrac{1}{2}) }^{1 + 2 + 3 + ... + 100} \cdot {2}^{5050} = \\ \\ \\ {( - \dfrac{1}{2} )}^{100 \cdot 101 \div 2} \cdot {2}^{5050} = \\ \\ \\ {( - \dfrac{1}{2}) }^{50 \cdot 101} \cdot {2}^{5050} = \\ \\ \\ {( - \dfrac{1}{2} )}^{5050} \cdot {2}^{5050} = \\ \\ \\ \dfrac{ {1}^{2050} }{ {2}^{5050} } \cdot {2}^{5050} = \\ \\ \\ \dfrac{ {2}^{5050} }{ {2}^{5050} }^{( {2}^{5050} } = 1$