.
$1)$
`S = 1 + 2^2 +2^4 +2^6 + ... + 2^{98} + 2^{100}`
`2^2S = 2^2 + 2^4 + 2^6 +2^8 + ... + 2^{100} + 2^{102}`
`=> 4S - S = 2^{102} - 1`
`=> 3S = 2^{102} - 1`
`=> S = {2^{102} - 1}/{3}`
$2)$
`S = 6^2 + 6^4 + 6^6 + ... + 6^98 + 6^{100}`
`=> 36S = 6^4 + 6^6 + ... + 6^{100} + 6^{102}`
`=> 36S - S = 6^{102} - 6^2`
`=> S = {6^{102] - 6^2}/{35}`
$3)$
`S = 1 +3^2 +3^4 + 3^6 + ... + 3^{100} + 3^{102}`
`9S = 3^2 + 3^4 + 3^6 + ... + 3^{102} +3^{104}`
`=> 8S = 3^{104} - 1`
`=> S = {3^{104} - 1}/8`