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Ufumbuzi - Mfulululizo wa kijiometri

Uwiano wa kawaida ni: r=−0.1111111111111111
r=-0.1111111111111111
Jumla ya mfululizo huu ni: s=−656
s=-656
Muundo mkuu wa mfululizo huu ni: an=−729⋅−0.1111111111111111n−1
a_n=-729*-0.1111111111111111^(n-1)
Neno la n la mfululizo huu ni: −729,81,−9,0.9999999999999998,−0.11111111111111109,0.012345679012345677,−0.0013717421124828527,0.00015241579027587253,−1.693508780843028E−05,1.8816764231589197E−06
-729,81,-9,0.9999999999999998,-0.11111111111111109,0.012345679012345677,-0.0013717421124828527,0.00015241579027587253,-1.693508780843028E-05,1.8816764231589197E-06
Tazama hatua

Njia Zingine za Kutatua

Mfulululizo wa kijiometri

Maelezo kwa hatua

1. Pata uwiano wa kawaida

Pata uwiano wa kawaida kwa kugawanya neno lolote la mlolongo kwa neno lililotangulia:

a2a1=81−729=−0.1111111111111111

a3a2=−981=−0.1111111111111111

a4a3=1−9=−0.1111111111111111

Uwiano wa kawaida (r) wa mlolongo ni thabiti na unasawa na sehemu ya maneno mawili yanayofuatana.
r=−0.1111111111111111

2. Pata jumla

5 ziada steps

sn=a*((1-rn)/(1-r))

Kupata jumla ya mfululizo, chomeka neno la kwanza: a=−729, uwiano wa kawaida: r=−0.1111111111111111, na idadi ya vipengele n=4 katika fomula ya jumla ya mfululizo wa kijiometri:

s4=-729*((1--0.11111111111111114)/(1--0.1111111111111111))

s4=-729*((1-0.00015241579027587256)/(1--0.1111111111111111))

s4=-729*(0.9998475842097241/(1--0.1111111111111111))

s4=-729*(0.9998475842097241/1.1111111111111112)

s4=−729⋅0.8998628257887517

s4=−656

3. Pata muundo mkuu

an=a⋅rn−1

Kupata muundo mkuu wa mfululizo, chomeka neno la kwanza: a=−729 na uwiano wa kawaida: r=−0.1111111111111111 katika fomula ya mfululizo wa kijiometri:

an=−729⋅−0.1111111111111111n−1

4. Pata neno la n

Tumia fomu kuu kupata kipimo cha nth

a1=−729

a2=a1·rn−1=−729⋅−0.11111111111111112−1=−729⋅−0.11111111111111111=−729⋅−0.1111111111111111=81

a3=a1·rn−1=−729⋅−0.11111111111111113−1=−729⋅−0.11111111111111112=−729⋅0.012345679012345678=−9

a4=a1·rn−1=−729⋅−0.11111111111111114−1=−729⋅−0.11111111111111113=−729⋅−0.001371742112482853=0.9999999999999998

a5=a1·rn−1=−729⋅−0.11111111111111115−1=−729⋅−0.11111111111111114=−729⋅0.00015241579027587256=−0.11111111111111109

a6=a1·rn−1=−729⋅−0.11111111111111116−1=−729⋅−0.11111111111111115=−729⋅−1.6935087808430282E−05=0.012345679012345677

a7=a1·rn−1=−729⋅−0.11111111111111117−1=−729⋅−0.11111111111111116=−729⋅1.8816764231589202E−06=−0.0013717421124828527

a8=a1·rn−1=−729⋅−0.11111111111111118−1=−729⋅−0.11111111111111117=−729⋅−2.090751581287689E−07=0.00015241579027587253

a9=a1·rn−1=−729⋅−0.11111111111111119−1=−729⋅−0.11111111111111118=−729⋅2.3230573125418763E−08=−1.693508780843028E−05

a10=a1·rn−1=−729⋅−0.111111111111111110−1=−729⋅−0.11111111111111119=−729⋅−2.581174791713196E−09=1.8816764231589197E−06

Kwa nini kujifunza hii

Mfululizo wa kijiometri hutumika kwa kawaida kuelezea dhana katika hisabati, fizikia, uhandisi, biolojia, uchumi, sayansi ya kompyuta, fedha, na zaidi, kufanya kuwa zana muhimu kuwa nayo katika vifaa vyetu. Moja ya matumizi ya kawaida ya safu za kijiometri, kwa mfano, ni kuhesabu riba iliyopatikana au isiyo kulipwa, shughuli inayohusishwa sana na fedha ambayo inaweza kumaanisha kupata au kupoteza pesa nyingi! Matumizi mengine ni pamoja na, lakini kwa hakika hayajazuiliwa, kuhesabu uwezekano, kupima radioactivity kwa muda, na kubuni majengo.

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