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Algebra Level 4

If s=1+4+18+96+600+.......2015 terms. Find remainder when s is divided by 10.

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The answer is 9.

Abhishek Sharma by Abhishek Sharma , 22, India

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1 solution

Raushan Sharma
Mar 28, 2016

Here, T r = r ⋅ r ! T_r = r \cdot r! , where T r T_r denotes the r r th term of the sequence.

Note that, when r ≥ 5 , r ⋅ r ! ≡ 0 ( m o d 10 ) r \geq 5, r \cdot r! \equiv 0 \pmod{10}

Hence, S ≡ 1 + 4 + 8 + 6 ≡ 19 ≡ 9 ( m o d 10 ) S \equiv 1 + 4 + 8 + 6 \equiv 19 \equiv 9 \pmod{10}

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