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16 Sep 2026, 02:01
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a = 3^(1/2 + 1/4 + 1/8 +....)
a + 3^[1/2(1 + 1/2 + 1/4 +...)]
1+ 1/2 + 1/4 + 1/8 + ... is an infinite geometric progression
The sum of an infinite GP is b/(1-r) where b = 1 and r = 1/2
So, the sum of the GP is 1/(1-1/2) = 2
=> a = 3^(1/2 x 2) = 3^1 = 3
Therefore, a = 3
a + 3^[1/2(1 + 1/2 + 1/4 +...)]
1+ 1/2 + 1/4 + 1/8 + ... is an infinite geometric progression
The sum of an infinite GP is b/(1-r) where b = 1 and r = 1/2
So, the sum of the GP is 1/(1-1/2) = 2
=> a = 3^(1/2 x 2) = 3^1 = 3
Therefore, a = 3
conty911
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