sequencessummations(編輯修改稿)
2024-11-29 17:11 本頁面
【文章內(nèi)容簡(jiǎn)介】 +…+n) = c + 2c +…+ nc r arjj ? 0n? ? arj ? 1j ? 0n? ? arkk ? 1n ? 1? ?arn ? 1? arkk ? 1n? ? arn ? 1? a ? arkk ? 0n?Telescoping Sums ( a jj ? 1n? ? a j ? 1 ) ? ( a 1 ? a 0 ) ? ( a 2 ? a 1 ) ?( a 3 ? a 2 ) ? ... ? ( a n ? a n ? 1 ) ? a n ? a 0[ k2k ? 14? ? ( k ? 1 )2] ?( 12? 02) ? ( 22? 12) ? ( 32? 22) ? ( 42? 32)42? 16 ? 0 ? 16Example Closed Form Solutions k ? n ( n ? 1 )2k ? 1n?A simple formula that can be used to calculate a sum without doing all the additions. Example: Proof: First we note that k2 (k1)2 = k2 (k22k+1) = 2k1. Since k2(k1)2 = 2k1, then we can sum each side from k=1 to k=n [ k 2k ? 1n? ? k ? 1?
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