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प्रश्न
Find the sum of the Geometric series 3 + 6 + 12 + …….. + 1536
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उत्तर
3 + 6 + 12 + …. + 1536
a = 3, r = `6/3` = 2
tn = 1536
a.rn–1 = 1536 ⇒ 3(2n–1) = 1536
2n–1 = `1536/3` ⇒ 2n–1 = 512
2n–1 = 29
∴ n – 1 = 9
n = 9 + 1 = 10
Number of terms = 10
Sn = `("a"("r"^"n" - 1))/("r" - 1)`
Sn = `(3(2^10 - 1))/(2 - 1)`
= `(3(1024 - 1))/1`
= 3 × 1023
= 3069
∴ Sum of the series is 3069
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