Question

a)A=2+2²+2³+2⁴+...+2¹⁰⁰
b)B=1+5+5²+5³+...+5¹⁵⁰
c)C=3+3²+3³+3¹⁰⁰⁰

ccan gap ạ hua k

Answer 1

a: \(2A=2^2+2^3+...+2^{101}\)

\(\Leftrightarrow A=2^{101}-2\)

b: \(5B=5+5^2+5^3+...+5^{151}\)

\(\Leftrightarrow4B=5^{151}-1\)

hay \(B=\dfrac{5^{151}-1}{4}\)

Answer 2

`A = 2 + 2^2 + ... + 2^100`

`=> 2A = 2^2 + 2^3 + ... + 2^101`

`=> 2A - A = (2^2 + 2^3 + ... + 2^101) - (2 + 2^2 + ... + 2^100)`

`=> A        = 2^101 - 2`

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`B = 1 + 5 + ... + 5^150`

`=> 5B = 5 + 5^2 + ... + 5^151`

`=> 5B-B = (5 + 5^2 + ... + 5^101) - (1 + 5 + ... + 5^150)`

`=> 4B     = 5^101 - 1`

`=>   B     = (5^101-1)/4`

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đề sai sửa lại đề :

`C = 3 + 3^2 + .... + 3^1000`

`=> 3C = 3^2 + 3^3 + ... + 3^1001`

`=> 3C - C = (3^2 + 3^3 + ... + 3^1001) - (3 + 3^2 + ... + 3^1000)`

`=> 2C     = 3^1001 - 3`

`=>   C     = (3^1001 - 3)/2`