BdMO National Higher Secondary 2004/4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Higher Secondary 2004/4

Unread post by samiul_samin » Wed Feb 21, 2018 5:53 pm

($a$)Find the sum of the series
$1+1^2.2+2^2+2^2.3+3^2.4+4^2+4^2.5+5^2.6+6^2$ upto ($2n+1$) terms.

($b$)Solve: $1+x+\dfrac {1.3}{2!} x^2+ \dfrac{1.3.5}{3!}x^3+.........=\sqrt 2$
Where the series on the left is convergent in a definite interval;find this interval.Write whether the series is convergent for $x=10$?

Confession
If it is already discussed in this forum,I am sorry.

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Higher Secondary 2004/4

Unread post by samiul_samin » Tue Feb 26, 2019 8:14 pm

(b)This a text book problem.Very easy one.
Answer:$x=-\dfrac 12$

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