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Given
S=1+2−122+3−2212+52−7242+17−12280+…, S = 1 + \frac{ \sqrt{2 } - 1 } { 2 \sqrt{2} } + \frac{ 3 - 2 \sqrt{2} } { 12} + \frac{ 5 \sqrt{2} - 7 } { 24 \sqrt{2} } + \frac{ 17 - 12 \sqrt{2} } {80 } + \ldots ,S=1+222−1+123−22+24252−7+8017−122+…,
find ⌈S⌉. \lceil S \rceil .⌈S⌉.
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