Putnam 1960 A3

Show that if $t_1 , t_2, t_3, t_4, t_5$ are real numbers, then $\sum_{j=1}^{5} (1-t_j )\exp \left( \sum_{k=1}^{j} t_k \right) \leq e^{e^{e^{e}}}.$

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