Răspuns: 2054
Explicație pas cu pas:
Salutare!
[tex]\bf (2^{n}+2^{n+1}+2^{n+2}+2^{n+3}+....+2^{n+10} ):2^{n} -2^{1^{2020}}=[/tex]
[tex]\bf 2^{n}\cdot (2^{n-n}+2^{n+1-n}+2^{n+2-n}+2^{n+3-n}+....+2^{n+10-n} ):2^{n} -2^{1}=[/tex]
[tex]\bf 2^{n}\cdot (2^{0}+2^{1}+2^{2}+2^{3}+....+2^{10} ):2^{n} -2=[/tex]
[tex]\bf 2^{n-n}\cdot (1+2+2^{2}+2^{3}+....+2^{10} ) -2=[/tex]
[tex]\bf 2^{0}\cdot (1+2+4+8+16+32+64+128+256+512+1024) -2=[/tex]
[tex]\bf 1\cdot 2056 -2=[/tex]
[tex]\boxed{\bf 2054}[/tex]
Am folosit următoarele formule pentru puteri
a⁰ = 1 sau 1 = a⁰
aⁿ : aᵇ = (a : a)ⁿ ⁻ ᵇ sau (a : a)ⁿ ⁻ ᵇ = aⁿ : aᵇ
aⁿ · bⁿ = (a · b)ⁿ sau (a · b)ⁿ = aⁿ · bⁿ
#copaceibrainly
