Question

Find the remainder when 5+ 5^2+5^3+.....+5^55
is divided by 13.​

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Asked on December 26, 2019 by

Rajiv Bhattacharya

Find the remainder when 1!+2!+3!+4!+....+n! divided by 15, if n≥5

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ANSWER

1!+2!+3!+4!+.........+n!

n≥5

when n=5

1!+2!+3+!+4!+5!=1+1×2+1×2×3+1×2×3×4+1×2×3×4×5

=1+2+6+24+120

=153 wherek=10

15

153

=15k+3 where k=10

when n=6

153+6!=153+720

15

873

=15k+3 where k=58

when n≥5, 3 is obtained as remainder when divided by 15