Ta có: \(\dfrac{1}{4}=\dfrac{10}{40}=\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}+\dfrac{1}{40}\)

Mà \(\dfrac{1}{31}>\dfrac{1}{40}\)

\(\dfrac{1}{32}>\dfrac{1}{40}\)

\(\dfrac{1}{33}>\dfrac{1}{40}\)

\(\dfrac{1}{34}>\dfrac{1}{40}\)

\(\dfrac{1}{35}>\dfrac{1}{40}\)

\(\dfrac{1}{36}>\dfrac{1}{40}\)

\(\dfrac{1}{37}>\dfrac{1}{40}\)

\(\dfrac{1}{38}>\dfrac{1}{40}\)

\(\dfrac{1}{39}>\dfrac{1}{40}\)

\(\Rightarrow\) \(\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{39}+\dfrac{1}{40}>\dfrac{10}{40}=\dfrac{1}{4}\)

Vậy \(S>\dfrac{1}{4}\)

\(A=1+3^2+3^4+...+3^{98}+3^{100}\)

\(3^2\cdot A=3^2+3^4+3^6+...+3^{100}+3^{102}\)

\(9A-A=\left(3^2+3^4+3^6+...+3^{100}+3^{102}\right)-\left(1+3^2+3^4+...+3^{98}+3^{100}\right)\)

\(8A=3^{102}-1\)

\(\Rightarrow A=\dfrac{3^{102}-1}{8}\)

A = 1 + 3² + 3⁴ + ..... + 3⁹⁸ + 3¹⁰⁰
3A = 3. ( 1 + 3² + 3⁴ + ..... + 3⁹⁸ + 3¹⁰⁰ )
3A = 3. 1 + 3. 3² + 3. 3⁴ + ..... + 3. 3⁹⁸ + 3. 3¹⁰⁰
3A = 3² + 3³ + 3⁴ + ..... + 3¹⁰⁰ + 3¹⁰¹
3A - A = ( 3² + 3³ + 3⁴ + ..... + 3¹⁰⁰ + 3¹⁰¹ ) - ( 1 + 3² + 3⁴ + ..... + 3⁹⁸ + 3¹⁰⁰ )
2A = 3¹⁰¹ - 1
A = ( 3¹⁰¹ - 1 ) : 2

Lời giải:

$A=1+32+34+....+398+400$

Từ $32$ đến $400$ có số số hạng là:

$(400-32):2+1=185$ (số hạng)

$32+34+....+398+400=(400+32).185:2=39960$

$\Rightarrow A=1+39960=39961$

Tham khảo

Ta có: 3A = 3.(1+3+32+33+...+399+3100)(1+3+32+33+...+399+3100)

3A = 3+32+33+...+3100+31013+32+33+...+3100+3101

Suy ra: 3A – A = (3+32+33+...+3100+3101)−(1+3+32+33+...+399+3100)(3+32+33+...+3100+3101)−(1+3+32+33+...+399+3100)

2A = 3101−13101−1

⇒⇒ A = 3101−123101−12

Vậy A = 3101−12

\(A=1-3+3^2-3^3+3^4-...-3^{98}-3^{99}+3^{100}\\ 3A=3-3^2+3^3-3^4-...-3^{98}+3^{99}-3^{100}+3^{101}\\ 3A-A=3^{101}-1\\ \Rightarrow A=\dfrac{3^{101}-1}{2}\)

A=3 mũ 101-1 phân số2

Các bạn giúp mình nhé

\(S=\left(1+3\right)+...+3^8\left(1+3\right)=4\left(1+...+3^8\right)⋮4\)

\(S=\left(1+3+3^2\right)+...+3^7\left(1+3+3^2\right)\)

\(=13\left(1+...+3^7\right)⋮13\)

\(S=1+3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9\)

\(S=\left(1+3\right)+\left(3^2+3^3\right)+\left(3^4+3^5\right)+\left(3^6+3^7\right)+\left(3^8+3^9\right)\)

\(S=4+3^2\left(1+3\right)+3^4\left(1+3\right)+3^6\left(1+3\right)+3^8\left(1+3\right)\)

\(S=4+3^2.4+3^4.4+3^6.4+3^8.4\)

\(S=4\left(3^2+3^4+3^6+3^8\right)\)

\(4⋮4\\ \Rightarrow4\left(3^2+3^4+3^6+3^8\right)⋮4\\ \Rightarrow S⋮4\)