\(A=1+5+5^2+5^3+.....+5^{49}+5^{50}\)

\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{50}+5^{51}\)

\(5A-A=\left(5+5^2+5^3+5^4+...+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+....+5^{49}+5^{50}\right)\)

\(\Rightarrow4A=5^{51}-1\)

\(A=\frac{5^{51}-1}{4}\)

A = 1 + 5 + 5² + .... + 5⁴⁹ + 5⁵⁰

5A = 5 + 5² + 5³ + ... + 5⁵⁰ + 5⁵¹

5A - A = (5 + 5² + 5³ + ... + 5⁵⁰ + 5⁵¹)  - (1 + 5 + 5² + .... + 5⁴⁹ + 5⁵⁰)

4A = 5⁵¹ - 1

\(A=\frac{5^{51}-1}{4}\)

ta có

5A=5+5^2+5^3+....+5^51

4A=5^51-1

A=(5^51-1)/4

A=...

A. Số lượng số hạng là:

\(\left(51-1\right):2+1=26\) (số hạng)

Tổng: \(\left(51+1\right)\times26:2=676\)

B. \(1-2+3-4+5-...+51\) 

\(=1+\left(-2+3\right)+\left(-4+5\right)+...+\left(-50+51\right)\)

\(=1+1+1+...+1\) 

Số lượng số hạng (không tính số 1 đầu tiên) là: 

\(\left(51-2\right):1+1=50\) (số hạng)

Số lượng cặp là: \(50:2=25\) (cặp) 

Tổng là: \(1+25\times1=26\)

good

TUI BẢO TÍNH THUẬN TIỆN MÀ

a)

\(A=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\)

\(5^2.A=5^2.\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)\)

\(25A=5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\)

\(A+25A=\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)+\left(5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\right)\)

\(26A=5^{22}-1\)

\(A=\dfrac{5^{22}-1}{26}\).

b)

\(26A+1=5^n\)

\(\Leftrightarrow\left(5^{52}-1\right)+1=5^n\)

\(\Leftrightarrow5^{52}=5^n\)

\(\Rightarrow n=52\).

c)

\(A=\left(5^{50}-5^{48}\right)+\left(5^{46}-5^{44}\right)+...+\left(5^6-5^4\right)+\left(5^2-1\right)\)

\(=5^{48}.\left(5^2-1\right)+5^{44}.\left(5^2-1\right)+...+5^4.\left(5^2-1\right)+1.\left(5^2-1\right)\)

\(=5^2.24.\left(5^{46}+5^{42}+...+5^2\right)+24\)

\(=25.4.6.\left(5^{46}+5^{42}+...+5^2\right)+24\)

\(=100.6.\left(5^{46}+5^{42}+...+5^2\right)+24⋮100\)

\(\Rightarrow A⋮100\).

Ta có : A = 1 + 5 + 5² + ...... + 5⁴⁹ + 5⁵⁰

=> 5A = 5 + 5² + 5³+..... + 5⁵⁰ + 5⁵¹

=> 5A - A = 5⁵¹ - 1

=> 4A = 5⁵¹ - 1

=> \(A=\frac{5^{51}-1}{4}\)

\(A=1+5+5^2+5^3+...+5^{49}+5^{50}\)

5A=\(5+5^2+5^3+...+5^{50}+5^{51}.\)

5A-A=\(\left(5+5^2+5^3+.....+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+...+5^{49}+5^{50}.\right)\)

4A=\(5^{51}-1\)

\(=>A=\frac{5^{51}-1}{4}\)

\(5A=5^1+5^2+5^3+...+5^{51}\)

\(4A=5A-A=5^{51}-1\)

\(\Rightarrow A=\frac{5^{51}-1}{4}\)