In the first week of the year, nancy saved $1. in each of the next 51 weeks, she saved $1 more than she had saved in the previous week. what was the total amount that nancy saved during the 52 weeks? $1,326

Nacy would save 1,378 dollar if she perofrm this saving plan.

Explanation:

It will be an Euler sum

In this case the last term is 52

Sn = 1.378‬

The explanation is that we can arrenge the term to generate sum of 53:

1 + 52

2 + 51

3 + 50

.......

25+28

26 + 27

In total there is 26 of this sums

53 x 26 = 1,378

If we notice 26 is half the value of n so we got:

we can also express 52 in term of n+1 achieving the Sn formula:

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