Is there a better way to find the sum of the below series than by traditional method (equating to constant say S and multiply with common ratio and subtract ) $S = 1-\frac{4}{3^1}+\frac{9}{3^2}-\frac{16}{3^3}+\frac{25}{3^4}-\frac{36}{3^5}+\cdots$
2026-03-26 06:20:11.1774506011
Quadratico geometric series
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Hint : General term of the series is given by $t_n=(-1)^{n+1}\cdot \frac {n^2}{3^{n-1}}$.
Now can you use the result of some common summations and evaluate $\sum_{n=1}^\infty t_n$?