Prove by PMI 3.2^2 +3^2.2^3 + 3^3.2^4 +----+  3^n.2^n+1 =   12/5(6^n  -1)

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S1=3×22=3×4=12=12561-1=125×5=12true for n=1for n=nSn=1256n-1for n=n+1summation=Sn+Tn+1=1256n-1+3n+12n+2=1256n-1+3n×3×2n×4=1256n-1+12×3n×2n=1256n-1+12×6n=12×6n-125+12×6n=12×6n-12+60×6n5=72×6n-125=12(6×6n-1)5=1256n+1-1=Sn+1hence proved by mathematical induction

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