しっしーのお計算ん向上委員会

計算の解説に究極特化してます。計算は、すっごくたのしい遊びだよ!!

計ササイズ-漸化式

漸化式 演習11

a1 = 2 , an+1 = 2an / ( 3an +4 ) a1 = 8 , an+1 = (an -9) / ( an -5 ) (ハイレベル) a1 = 1 , an+1 = (3an +6 ) / ( an +4 ) (ハイレベル) a1 = 2 , a2 = 3 , an+2 -2an+1 -8an =0 a1 = 2 , a2 = 7 , an+2 -3an+1 +2an =0 a1 = 1 , a2 = 5 , an+2 -6an+1 …

漸化式 演習10

a1 = 3 , an+1 an -2an+1 + 2an =0 a1 = 5 , an+1 = 3an +4 a1 = 1 , an+1 = 2an +3n-1 a1 = 2 , an+1 = 2an + n2 -2n-3 a1 = 5 , an+1 = 2an +3n a1 = 1 , nan+1= (n+1)an a1 = 1 , an+1 = (n+1)an +n (ハイレベル) a1 = 2 , an+1 an =2√an nΣk=1 ak = 3an …

漸化式 演習9

a1 = 1 , b1 = 0 , an+1 = 5an +4bn , bn+1 = an +5bn (ハイレベル) a1 = 2 , an+1 = 3an +2n2 -2n-1 a1 = 1 , an+1 - 2an = n・2n+1 a1 = 1 , an+1 = (1/2)an + (n-1) / {n(n+1)} (ハイレベル) a1 = 8 , an = an-1 / { (n-1)an-1 +1 } (n≧2) a1 = 3 , an an…

漸化式 演習8

a1 = 1 , 2an+1 = 3an +2 nΣk=1 ak (ハイレベル) a1 = 1 , an+1 = 2an +3 a1 = 1 , an+1 = 2an + (-1)n a1 = 1 , a2 = 1 , an+2 - an+1 -2an =0 a1 = 2 , an+1 = (an -1) / (3 +an ) +1 (ハイレベル) a1 = 1 , a2 = 2 , an+2 - 2an+1 +an =2 (bn = an+1 - an…

漸化式 演習7

a1 = 1 , a2 = 2 , an+2 - 6an+1 +9an =0 a1 = 1 , a2 = 2 , an+2 = an+1 +an (ハイレベル) a1 = 1 , b1 = 3 , an+1 = 3an +bn , bn+1 = 2an +4bn (ハイレベル) a1 = 2 , an+1 = 2an -1 a1 = -8 , an+1 - an = 2n-1 a1 = 0 , an+1 = -2an + (-1)n a1 = 2 , n…

漸化式 演習6

a1 = 1 , an+1 = 3an + 2n a1 = 2 , ( an+1 )2 = 4(an)3 a1 = 1 , nan+1 = (n+1)an +1 a1 = 2 , 3nan+1 = (n+1)an a1 = 1 , (n+3)an+1 = nan a1 = 1/2 , an+1 = an / ( 2- an ) a1 = 8 , an+1 = ( 3an +2 ) / ( an +2 ) (ハイレベル) a1 = 1 , a2 =2 , an+2 …

漸化式 演習5

nΣk=1 ak = Sn = 2an + n a1 = r , an+1 = r+(1/r)an (rは0以外の実数、ハイレベル) a1 = 1 , a2 =3 , an = √ (an+1 an-1) (n≧2) (ハイレベル) a1 = 1 , a2 =1/2 , an = 2an+1 an-1 / (an+1 + an-1) (n≧2) (ハイレベル) a1 = 1/2 , a2 =1/3 , an+2 = an an+1…

漸化式 演習4

a1 = 2/3 , ( n+2 )an = ( n-1)an-1 (n≧2) a1 = 0 , a2 =1 , 5an+2 = 3an+1 +2an a1 = 1 , a2 =2 , an+2 -2an+1 -3an =0 a1 = 0 , a2 =3 , an+2 -6an+1 +9an =0 a1 = 1 , b1 =3 , an+1 = 3an + bn , bn+1 = 2an + 4bn (ハイレベル) a1 = -1 , b1 =1 , an+1 =…

漸化式 演習3

nΣk=1 ak =Sn = -2an -2n+5 a1 = 2 , an+1 = an -1/2 a1 = -1 , an+1 +an =0 a1 = 3 , 2an+1 -2an =4n2 +2n-1 a1 = 2 , an+1 =3an -2 a1 = 3 , 2an+1 -an +2 =0 a1 = -2 , an+1 = -3an -4n+3 a1 = 4 , an+1 = 4an -2n+1 a1 = 1 , an+1 = 3an / ( 6an +1 ) a1…

漸化式 演習2

今回の問は全てレベル高いです。 だから1つも解けないとしても、落ち込まなくて大丈夫です。 「こういうものもある」ぐらいの認識で構いません。 で、復習してモノにしましょう。 a1 = 1/2 , (n+1)an = (n-1)an-1 (n≧2) a1 = 1 , a2 = 2 , an+2 +4an+1 -5an …

漸化式 演習1

a1 = -3 , an+1 = an +4 a1 = 4 , 2an+1 + 3an =0 a1 = 1 , an+1 = an +2n -3n+1 a1 = 6 , an+1 = 2an -3 a1 = 1 , an+1 = 3an +4n a1 = 3 , an+1 = 2an +3n+1 a1 = 1/5 , an+1 = an / ( 4an -1 ) a1 = 1 , an+1 = 2√an a1 = 2 , an+1 = { (n+2) / n } an +1…