Toán Cho B = 2 + 2² + 2³ + 2⁴ + … + 2¹⁰⁰ Tính C = 5 – 2¹⁰⁰ + B 01/07/2021 By Raelynn Cho B = 2 + 2² + 2³ + 2⁴ + … + 2¹⁰⁰ Tính C = 5 – 2¹⁰⁰ + B
Đáp án: Giải thích các bước giải: $B=2+2^2+2^3+2^4+…+2^{100}\\\Leftrightarrow 2B=2^2+2^3+2^4+2^5+…+2^{101}\\\Leftrightarrow 2B-B=2^{101}-2=B\\\Rightarrow C=5-2^{100}+2^{101}-2\\=2^{100}(2-1)+3\\=2^{100}+3$ Trả lời
`B=2+2^2+2^3+………..+2^{100}` `2B=2^2+2^3+2^4+………..+2^{101}` `2B-B=(2^2+2^3+2^4+………..+2^{101})-(2+2^2+2^3+………..+2^{100})` `B=2^{101}-2` `C=5-2^{100}+B` `C=5-2^{100}+2^{101}-2` `C=2^{100}(2-1)+(5-2)` `C=2^{100}+3` Vậy `C=2^{100}+3` Trả lời
Đáp án:
Giải thích các bước giải:
$B=2+2^2+2^3+2^4+…+2^{100}\\\Leftrightarrow 2B=2^2+2^3+2^4+2^5+…+2^{101}\\\Leftrightarrow 2B-B=2^{101}-2=B\\\Rightarrow C=5-2^{100}+2^{101}-2\\=2^{100}(2-1)+3\\=2^{100}+3$
`B=2+2^2+2^3+………..+2^{100}`
`2B=2^2+2^3+2^4+………..+2^{101}`
`2B-B=(2^2+2^3+2^4+………..+2^{101})-(2+2^2+2^3+………..+2^{100})`
`B=2^{101}-2`
`C=5-2^{100}+B`
`C=5-2^{100}+2^{101}-2`
`C=2^{100}(2-1)+(5-2)`
`C=2^{100}+3`
Vậy `C=2^{100}+3`