BdMO National Higher Secondary 2004/4
Posted: 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
$1+1^2.2+2^2+2^2.3+3^2.4+4^2+4^2.5+5^2.6+6^2$ 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