1+5+13+29+61+.............n terms then find sum to n terms

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Please find below the solution to the asked query:

S=1+5+13+29+61+........+Tn-1+TnS=       1+5+13+29+61+........+Tn-1+TnSubtracting the above two equations we get,0=1+4+8+16+32+.........+     Tn-Tn-1-TnTn=1+4+8+16+32+.........+     Tn-Tn-1n-1 terms4+8+16+32+......... is a G.P. of n-1 terms having first terma=2 andcommon ratior=2Sum=42n-1-12-1=222n-1-1=22.2n-1-22=2n-1+2-4=2n+1-4Tn=1+2n+1-4Tn=2n+1-3Sn=n=1n=n Tn=n=1n=n 2n+1-3=n=1n=n 2n+1-3n=1n=n1=22+23+24+......+2n+1-31+1+1+1+....n times=222n-12-1-3n=22.2n-22-3nSn=2n+2-4-3nHence sum of S=1+5+13+29+61+.... upto n terms is 2n+2-3n-4.

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