`A = 1 + 3 + 3^2 + 3^3 + ... + 3^101`
`A = ( 1 + 3 + 3^2 )( 3^3 + 3^4 + 3^5 ) + ... + (3^99 + 3^100 + 3^101)`
`A= (1 + 3 + 3^2)1 + 3^3(1 + 3 + 3^2) + ... + 3^99 ( 1 + 3+ 3^2)`
`A = ( 1 + 3 + 9 ) ( 1 + 3^3 + ... + 3^99)`
`A = 13(1+3^3 + ... + 3^99)` `\vdots` `13` `(dpcm)`
A=1+3+32+33+...+3101A=1+3+32+33+...+3101
A=(1+3+32)(33+34+35)+...+(399+3100+3101)A=(1+3+32)(33+34+35)+...+(399+3100+3101)
A= (1+3+32)1+33(1+3+32)+...+399(1+3+32)A= (1+3+32)1+33(1+3+32)+...+399(1+3+32)
A=(1+3+9)(1+33+...+399)A=(1+3+9)(1+33+...+399)
A=13(1+33+...+399)A=13(1+33+...+399) ⋮⋮ 1313 (dpcm)
