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Question

If (10)9+2(11)1(10)8+3(11)2(10)7+...+10(11)9=k(10)9, then k is equal to :

A
12110
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B
441100
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C
100
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D
110
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Solution

The correct option is C 100
(10)9+2(11)1(10)8+3(11)2(10)7+...+10(11)9=k(10)9
k=1+2(1110)+3(1110)2+...+10(1110)9...(1)
Multiply equation (1) with 1110
1110k=1110+2(1110)2+3(1110)3+...+9(1110)9+10(1110)10
Substracting equation (2) from equation (1)
k10=1+1110+(1110)2+(1110)3+...+(1110)910(1110)10
k10=1[(1110)101]1110110(1110)10
k=100

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