Question

can you please explain a and b thanks

Fourier Analysis

See are two finite sequences of complex numben 7. Suppose (an)- and (bn)1 Let Br= bn denote the partial sums of the series b with the conventicn 1 Bo=0. (a) Prove the summation by parts formula N-1 anbn aNBN- aM BM-1 (an+1-an)B n M n-M (b) Deduce from this formula Dirichlet's test for convergence of a series: if the partial sums of the seriesb are bounded, and fan} is a sequence of real numbers that decreases monotonically to 0, thenabn converges.

Answer 1

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