Câu hỏi của trinh mai hoang linh

Question

Cho A=2+22+23+24+...+290Chứng minh rằng A chia hết cho 21Ai nhanh mik tik,mik cảm ơn trước^^^Kết bn mik nha

Nguyệt · Accepted Answer

$A=\left(2+2^2+2^3+2^4+2^5\right)+$$\left(2^6+2^7+2^8+2^9+2^{10}\right)+....\left(2^{86}+2^{87}+2^{88}+2^{89}+2^{90}\right)$$A=2.\left(1+2+2^2+2^3+2^4\right)+2^6.\left(1+2+2^2+2^3+2^4\right)$$+....+2^{86}.\left(1+2+2^2+2^3+2^4\right)$$A=2.21+2^6.21+...+2^{86}.21$$A=21.\left(2+2^6+...+2^{86}\right)⋮21$Câu trả lời: $A=\left(2+2^2+2^3+2^4+2^5\right)+$$\left(2^6+2^7+2^8+2^9+2^{10}\right)+....\left(2^{86}+2^{87}+2^{88}+2^{89}+2^{90}\right)$$A=2.\left(1+2+2^2+2^3+2^4\right)+2^6.\left(1+2+2^2+2^3+2^4\right)$$+....+2^{86}.\left(1+2+2^2+2^3+2^4\right)$$A=2.21+2^6.21+...+2^{86}.21$$A=21.\left(2+2^6+...+2^{86}\right)⋮21$

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