oblicz

[mol_ksiazkowy]

\(\displaystyle{ s= \sum_{k=1}^{2007} a_kg_k}\)
\(\displaystyle{ a_k=2k-1}\)
\(\displaystyle{ g_k=2^k}\)

[max]

Niech \(\displaystyle{ G_{k} = \sum_{l = 1}^{k}g_{l} = 2^{k + 1} - 1}\)
wtedy:
\(\displaystyle{ \sum_{k = 1}^{n}a_{k}g_{k} = \sum_{k = 1}^{n - 1}(a_{k} - a_{k + 1})G_{k} + a_{n}G_{n} = \ldots}\)
https://matematyka.pl/viewtopic.php?t=18 ... 6%E6+abela

[mol_ksiazkowy]

\(\displaystyle{ s=\frac{g_{n+2}a_n- g_{n+1}a_{n+1}-g_2a_0+ g_1a_1}{(r-1)^2}}\)