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The process of the third problem in mathematics
)by AnBN+ 1-an+ 1bn+2bn+ 1bn = 0,cn=

One; one

billion

, the sequence {cn} is a arithmetic progression with 1 as the first term and a tolerance of 2, and the general term formula of the sequence {cn} can be obtained;

(2) Dislocation subtraction summation.

( 1)∵anbn+ 1? an+ 1bn+2bn+ 1bn=0,cn=anbn,

∴cn? cn+ 1+2=0,

∴cn+ 1? cn=2,

∫ Two series whose first term is 1 {an}, {bn}

∴ Sequence {cn} is a arithmetic progression, the first term is 1, and the tolerance is 2.

∴cn=2n? 1;

(2)∵bn=3n? 1,cn=anbn,

∴an=(2n? 1)? 3 1? n,

∴Sn= 1×30+3×3? 1+…+(2n? 1)×3 1? n,

∴3Sn= 1×3+3×30+…+(2n? 1)×32? n,

∴? 2Sn=? 1×3? 2? (30+3? 1+…+32? n)? (2n? 1)? 3 1? n,

∴Sn=(n? 1)3 1? n+3。