Answer to Question #67003 in Real Analysis for koel

Question

(a) Find the sum of the series
VT).
+ + + ,
./ v (n + 3)3 11(n + 6)3 V[n 3 (n — 1)]3
3
(b) By showing that the remainder after n-terms
tends to zero, find Maclaurin's series
expansion of sin 2x. 5
(c) Prove that the function f defined on [0, 1] by
f(x) = (— 1)n+1for 1
< x < ,
n + 1
n = 1, 2, 3, ... is integrable on [0, 1].