MathCastle
Differential EquationsEasySeries Solutions

Series Solutions · Easy problem

With y=∑n=0∞anxny = \sum_{n=0}^{\infty} a_n x^n, the second derivative ∑n=2∞n(n−1)anxn−2\sum_{n=2}^{\infty} n(n-1)a_n x^{n-2} is rewritten after an index shift as ∑k=0∞ckxk\sum_{k=0}^{\infty} c_k x^k. If a5=2a_5 = 2, find c3c_3.