- #1
spectrum123
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here is the Q. i want a general term for Ʃx^(-1) for which limits are x from 0 to n
or simply a general term for 1-1+2-1+3-1+4-1+... till n
or simply a general term for 1-1+2-1+3-1+4-1+... till n
spectrum123 said:ok thanks but i didn't get the result?
The symbol "Ʃ" represents the summation notation, meaning that the expression following it should be summed up for each value of x from 0 to n.
To solve for limits using this notation, you can first rewrite it as a series expression: Ʃx^(-1) = 1 + 1/2 + 1/3 + ... + 1/n. Then, you can use known series or integral tests to determine if this series converges or diverges.
The expression x=0 to n specifies the range of values for x that should be included in the summation. In this case, we are summing up the expression Ʃx^(-1) for all values of x from 0 to n.
This limit notation can be used for any function, as long as it can be expressed as a series. However, not all functions can be easily transformed into a series, so it may not always be applicable.
If the series expression resulting from the summation converges, then the limit will be a finite value. If the series diverges, then the limit will be infinite.