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Geometric Progression 



Problem 14 of 23 


14. `1 + x^4 + 3^2 + 4 + x^6 + 6^2 + 7 + x^8 + 9^2 + ... 3n` terms










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Geometric Progression 
14. `1 + x^4 + 3^2 + 4 + x^6 + 6^2 + 7 + x^8 + 9^2 + ... 3n` terms
`S_(3n) = 1 + x^4 + 3^2 + 4 + x^6 + 6^2 + 7 + x^8 + 9^2 + ... 3n` terms
`= (1 + 4 + 7 + ... n " terms") + (x^4 + x^6 + x^8 + ... n " terms") + (3^2 + 6^2 + 9^2+ ... n " terms")`
`= (1 + 4 + 7 + ... n " terms") + x^4 (1 + x^2 + x^4 + ... n " terms") + 3^2 (1 + 2^2 + 3^2 + ... n " terms")`
`= n/2 [ 2 × 1 + (n  1) × 3 ] + x^4 [ (x^2)^n  1 ] / ( x^2  1) + 9 × n/6 (n + 1) (2n + 1)`
`= n/2 (3n  1) + x^4 (x^(2n)  1) / ( x^2  1) + (3n)/2 (n + 1) (2n + 1)`





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