設a1=22-02,a2=32-12,…,an=(n+1)2-(n-1)2(n為大於1的整數)(1)計算a15...
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問題詳情:
設a1=22-02,a2=32-12,…,an=(n+1)2-(n-1)2(n為大於1的整數)
(1)計算a15的值;
(2)通過拼圖你發現前三個圖形的面積之和與第四個正方形的面積之間有什麼關係:
__________________________________(用含a、b的式子表示);
① ② ③ ④
(3)根據(2)中結論,探究an=(n+1)2-(n-1)2是否為4的倍數.
【回答】
(1)a15=162-142=256-196=60·······································································(2分)
(2) (a+b)2=a2+2ab+b2 ··············································································(4分)
(3) an=(n+1)2-(n-1)2 =(n2+2n+1)-(n2-2n+1) =n2+2n+1-n2+2n-1=4n
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是4的倍數. ···············································································(6分)
知識點:有理數的乘方
題型:解答題