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Mathematics Senior High

書き込みがある波線部で、 式を変形したら右のようになりますよね? なぜn≧2という条件がつかないのですか?

1 基本例題 96 (等差)×(等比)型の数列の和 一般項が (2n-1) 3"-' で表される数列の初項から第n項までの和 S=1・1+3・3+5・32+………+(2n-1)・3n-1 を求めよ。 CHART SOLUTION 解答) よって MIESTOROC (等差)×(等比)型の数列の和 S s-rs を作る (rは公比) ...・・・ 数列の一般項は an=(2n-1)・3-1 これは等比数列ではないが等比数列に似た 形である。 等比数列 αrn-1 の和は S=a+ar+ar² +. FILOFF -2S=1+2(3+32+ ここで ゆえに rS= artare+...... tarn-1+arn の辺々を引いて (1-r) S=a(1-r") から求めた。 この例題でも,同じ方針で S-3S を計算する。 (2n-3)-3-2 両辺に3を掛けると S=1・1+3・3+5・32+……‥+(2n-1)・37-1 AE)(I-SE) | 第 (n-1) 項は 3n) 12(n-1)-3(p-de)−(S+AE)_ _ __ 3S= 1・3+3・32+.....+(n-3)・3-1+(2n-1)・3 辺々を引くと ■S-3S=1・1+2・3 +2・3+…・・・・・+2・3-1 したがって tarn-1 3+3+ ...... +3n-1= NE +32+ 15 一 ¥3n-¹)-(2n−1)• 3″ 3(3-1-1)_3 3-1 = ← 2 -2S=1+2.0(3"-1-1)-(2n-1)・3” =1+3"-3-(2n-1).3" =(2-2n)・3-2 S=(n-1)・3"+1 -(2n-1).3″ & 引き算しやすい位置に項を書く。 TE ty -(3-1-1) 0000 130 provede ²+ a=Si 計算しやすいように の項を,上下にそろえて 書く。 (2n-1)・3”である。 符号のミスに注意。 ( )が等比数列になる。 初項3,公比3, 数 n-1の等比数列の和。 n=1,2 を代入して検算 しておくとよい。

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English Senior High

英語リーディングの共通テスト大門3のB 4つの選択肢を並べるような問題が苦手で、対策問題集を解いている時にいつもどこかしら間違えてしまいます。時間制限を決めつつ、正しい答えを選ぶことがとても難しい状態です。 どのように考えれば良いでしょうか。 また模試などでは、時間と正確... Read More

B You enjoy outdoor sports and have found an interesting story in a mountain climbing magazine. Attempting the Three Peaks Challenge By John Highland Last September, a team of 12 of us, 10 climbers and two minibus drivers, participated in the Three Peaks Challenge, which is well known for its difficulty among climbers in Britain. The goal is to climb the highest mountain in Scotland (Ben Nevis), in England (Scafell Pike), and in Wales (Snowdon) within 24 hours, including approximately 10 hours of driving between the mountains. To prepare for this, we trained on and off for several months and planned the route carefully. Our challenge would start at the foot of Ben Nevis and finish at the foot of Snowdon. Ben Nevis (▲1344 m) Scafell Pike (▲977 m) Snowdon (▲1085 m) We began our first climb at six o'clock on a beautiful autumn morning. Thanks to our training, we reached the summit in under three hours. On the way down, however, I realised I had dropped my phone. Fortunately, I found it with the help of the team, but we lost 15 minutes. We reached our next destination, Scafell Pike, early that evening. After six hours of rest in the minibus, we started our second climb full of energy. As it got darker, though, we had to slow down. It took four-and-a-half hours to complete Scafell Pike. Again, it took longer than planned, and time was running out. However, because the traffic was light, we were right on schedule when we started our final climb. Now we felt more confident we could complete the challenge within the time limit. Unfortunately, soon after we started the final climb, it began to rain heavily and we had to slow down again. It was slippery and very difficult to see ahead. At 4.30 am, we realised that we could no longer finish in 24 hours. - 16- (2110-16)

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