I see that derivative of y with respect to x is just like the ratio of y over x.(adsbygoogle = window.adsbygoogle || []).push({});

But, Why U_{n}(the formula to find nth term) isnotthe derivative of S_{n}(the sum of sequence formula) ??

For example,

1 2 5 10 -> y = x^{2}+1

+1 +3 +5 -> y= 2x-1

+2 +2 -> y=2

I think that the second level is 2x (since it's the derivative of y = x^{2}+1), but it's not...

Derivative of y with respect to x is just like how much y will gain with x gaining, right ?

Is there any way or formula to correlate the derivative of S_{n}with U_{n}??

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# Sequence and Derivative

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