First slide

Geometric progression

Question

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

Moderate

A

a = b + c
B

a = bc
C

b = ac
D

c = ab

Solution

$\begin{array}{l} a = 1 + 10 + 10^{2} + \dots . + 10^{54} \\ = \frac{10^{55} - 1}{10 - 1} = \frac{10^{55} - 1}{10^{5} - 1} \times \frac{10^{5} - 1}{10 - 1} = b c \end{array}$

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