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Question
The remainder when 445+444+443+442+441+...........+40 is divided by 17 is:-
Options:
A .  5
B .  4
C .  1
D .  None of these
Answer: Option A
:
A
Sn=40+41+42+43+...................+443+444+445
Sn=(1+4+16+64)+44(1+4+16+64)+..............+440(1+4+16+64)+444+445
All the terms except 444+445 are divisible by 17 (as 1 + 4 + 16 + 64 = 85 which is a multiple of 17).
Now, 445+44417=444(4+1)17=(44)11×517=(255+1)11×517=111×517=517.
Hence the required remainder is 5.

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