1. Tardigrade
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  4. Let a=111 ldots 1(55 digits ) b=1+10+102+ ldots+104 c=1+105+1010+1015+ ldots+1050, then

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Q. Let $a=111 \ldots 1(55$ digits $)$
$ b=1+10+10^{2}+\ldots+10^{4}$
$ c=1+10^{5}+10^{10}+10^{15}+\ldots+10^{50}$, then

Sequences and Series

Solution:

$ a=1 +10+10^{2}+\ldots+10^{54} $
$=\frac{10^{55}-1}{10-1}=\frac{10^{55}-1}{10^{5}-1} \cdot \frac{10^{5}-1}{10-1}=b c $