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Well, it is a difficult sequence, or rather sequences! There are actually 99 sequences that you have to sum up individually, and then take the sum of ALL the sums!.

They go like this:
2 + 3 + 4 + 5........100 - with 99 terms and comm. diff=1
6 + 8 + 10 + 12....100 - with 98 terms and comm. diff=2
12 + 15 + 18 +......100 - with 97 terms and comm. diff=3
And so on till: 99 x 100 =9900 - being the sum of the last sequence.
Only a spreadsheet or a computer code could sum them up for you. I wrote a short computer code that sums them up as follows:
5049 +  10094 +  15132 +  20160 +  25175 +  30174 +  35154 +  40112 +  45045 +  49950 +  54824 +  59664 +  64467 +  69230 +  73950 +  78624 +  83249 +  87822 +  92340 +  96800 +  101199 +  105534 +  109802 +  114000 +  118125 +  122174 +  126144 +  130032 +  133835 +  137550 +  141174 +  144704 +  148137 +  151470 +  154700 +  157824 +  160839 +  163742 +  166530 +  169200 +  171749 +  174174 +  176472 +  178640 +  180675 +  182574 +  184334 +  185952 +  187425 +  188750 +  189924 +  190944 +  191807 +  192510 +  193050 +  193424 +  193629 +  193662 +  193520 +  193200 +  192699 +  192014 +  191142 +  190080 +  188825 +  187374 +  185724 +  183872 +  181815 +  179550 +  177074 +  174384 +  171477 +  168350 +  165000 +  161424 +  157619 +  153582 +  149310 +  144800 +  140049 +  135054 +  129812 +  124320 +  118575 +  112574 +  106314 +  99792 +  93005 +  85950 +  78624 +  71024 +  63147 +  54990 +  46550 +  37824 +  28809 +  19502 +  9900 = 12,582,075.
Alternatively, there is a pattern called "closed form" that applies to every term above and it looks like this:
5050*n - 1/2 * [n^3 + n^2]. Example: First term:
5050*1 - 1/2 * [1^3 + 1^2] =5050 - 1 =5049. And with this "closed form" you can use any calculator that has sigma(∑) built into it and sum them all up. You should get the same total as above:12,582,075.

Mar 7, 2019
Mar 6, 2019

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