Need help on the entire page please For the following telescoping series find a

Question

Need help on the entire page please For the following telescoping series find a formula for the nth term of the sequence of partial sum {S_n} and then evaluate the value of lim_x rightarrow infinity S_n to obtain the value of the series or state if it diverges. sigma_k = 1^infinity (1/k + 2 - 1/k + 3) For the following function: f(x) = 1/x, a = 1 Find the linear approximating polynomial centered at "a" Find the quadratic approximating polynomial centered at "a" Use the polynomials(both linear and quadratic) to approximate the value of 1/1.05 Find the nth order Taylor polynomial for f(x) = e^-x centered at "0" for n= 0.1, 2

Explanation / Answer

14) k=1 to (1/(k+2) -1/(k+3))

sk=(1/(1+2) -1/(1+3))+(1/(2+2) -1/(2+3))+................+(1/(k+2) -1/(k+3))

sk=(1/3 -1/4)+(1/4 -1/5)+................+(1/(k+2) -1/(k+3))

sk=1/3 -1/(k+3)

limk->1/3 -1/(k+3)

=1/3 -1/

=1/3 -0

=1/3

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