( 1 3 + 4 7 ) + ( 1 3 2 + 1 3 × 4 7 + 4 2 7 2 ) + ( 1 3 3 + 1 3 2 × 4 7 + 1 3 × 4 2 7 2 + 4 3 7 3 ) + ? upto infinite terms, is equal to [2026]

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Solution

Q.
$(\frac{1}{3} + \frac{4}{7}) + (\frac{1}{3^{2}} + \frac{1}{3} \times \frac{4}{7} + \frac{4^{2}}{7^{2}}) + (\frac{1}{3^{3}} + \frac{1}{3^{2}} \times \frac{4}{7} + \frac{1}{3} \times \frac{4^{2}}{7^{2}} + \frac{4^{3}}{7^{3}}) + \dots$ upto infinite terms, is equal to [2026]

1 $\frac{6}{5}$

2 $\frac{4}{3}$

3 $\frac{7}{4}$

4 $\frac{5}{2}$

Ans.
(4)

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