Best of Series

Number Theory Level pending

Find out the value of positive integer n for all 1 million terms of a specific series (called HCR’s Series) as given below n!=1+1×1!+2×2!+3×3!+ …….+999998×999998!+999999×999999!


The answer is 1000000.

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1 solution

Sunil Pradhan
Mar 31, 2014

Let p = 1 × 1! + 2 × 2! ... + n × n! = (n + 1)! – 1!

so p + 1 = 1 + 1 × 1! + 2 × 2! ... + n × n! = 1 + (n + 1)! – 1! = (n + 1)!

n!=1+1×1!+2×2!+3×3!+ …….+999998×999998!+999999×999999!

= (999999 + 1)! = 1000000!

n = 1000000

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