Guest Session: 1 Question Remaining. Create Account to save progress.
Login
Infinite Seriesmedium
0:00.0

If two series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞​an​ and ∑n=1∞bn\sum_{n=1}^{\infty} b_n∑n=1∞​bn​ both converge absolutely with sums AAA and BBB respectively, the Cauchy product ∑n=1∞cn\sum_{n=1}^{\infty} c_n∑n=1∞​cn​ where cn=∑k=1nakbn+1−kc_n = \sum_{k=1}^{n} a_k b_{n+1-k}cn​=∑k=1n​ak​bn+1−k​ satisfies: