Aditi Chauhan
Last Activity: 10 Years ago
Hello Student,
Please find the answer to your question
an = 3/4 –(3/4)2 + (3/4)3 + …… + (-1)n-1 (3/4)n
=
= 3/7 (1 – (-3/4)
n)
Bn = 1 – an and bn > an ∀ n ≥ no
∴ 1 – an> an ⇒ 2an < 1
⇒
[1 –(
)
n] < 1 ⇒ - (
)
n < 1/6
⇒ (-3)n+1 < 22n-1
For n to be even, inequality always holds. For n to be odd, it holds for n ≥ 7.
∴ The least natural no, for which it holds is 6
( ∵ it holds for every even natural no.)
Thanks
Aditi Chauhan
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