6 3 26 + 10 · 1 3 25 + 10 · 2 3 24 + 10 · 2 2 3 23 + ? + 10 · 2 24 3 is equal to: [2026]

Question

$\frac{6}{3^{26}} + \frac{10 \cdot 1}{3^{25}} + \frac{10 \cdot 2}{3^{24}} + \frac{10 \cdot 2^{2}}{3^{23}} + \dots + \frac{10 \cdot 2^{24}}{3}$ is equal to: [2026]

Smart Achievers · Accepted Answer

(3)

$S = \frac{6}{3^{26}} + \frac{10}{3^{25}} [\frac{6^{25} - 1}{6 - 1}]$

$S = \frac{6}{3^{26}} + \frac{10}{3^{25}} [\frac{6^{25} - 1}{5}]$

$S = \frac{2}{3^{25}} + 2 [\frac{2^{25}}{3^{25}} - \frac{1}{3^{25}}]$

$S = 2^{26}$

Solution

Q.
$\frac{6}{3^{26}} + \frac{10 \cdot 1}{3^{25}} + \frac{10 \cdot 2}{3^{24}} + \frac{10 \cdot 2^{2}}{3^{23}} + \dots + \frac{10 \cdot 2^{24}}{3}$ is equal to: [2026]

1 $2^{25}$

2 $3^{26}$

3 $2^{26}$

4 $3^{25}$

Ans.
(3)

$S = \frac{6}{3^{26}} + \frac{10}{3^{25}} [\frac{6^{25} - 1}{6 - 1}]$

$S = \frac{6}{3^{26}} + \frac{10}{3^{25}} [\frac{6^{25} - 1}{5}]$

$S = \frac{2}{3^{25}} + 2 [\frac{2^{25}}{3^{25}} - \frac{1}{3^{25}}]$

$S = 2^{26}$

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Solution

Q. 6326+10·1325+10·2324+10·22323+⋯+10·2243 is equal to: [2026]

1 225

2 326

3 226

4 325

Ans. (3) S=6326+10325[625-16-1] S=6326+10325[625-15] S=2325+2[225325-1325] S=226