Write the answer using summation or product notation (1^{3}-1)-(2^{3}-1)+(3^{3}-1)-



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Write the answer using summation or product notation

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-08-13Added 88 answers

Step 1
The given sum is (131)(231)+(331)(431)+(531).
The above sum has 5 terms.
The second and the fourth terms have a negative sign before them.
Each term inside the bracket are obtained by subtracting 1 from the cube of the nth natural number.
Thus, even terms have a negative sign while odd terms have a positive sign.
(131)=n31 where n=1
(231)=n31 where n=2
(331)=n31 where n=3
(431)=n31 where n=4
(531)=n31 where n=5
Step 2
Use the expression (1) to get negative sign before even terms and positive sign before odd terms. For the given sum n varies from 1 to 5.
Hence, the above sum can be rewritten using summation as follows.
The above sum can be separated using odd terms and even terms as follows.
The given sum can be represented using summation as n=15(1)n(n31).

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