Q

[Sangam]

1 = 1,
1 − 4 = −(1 + 2)
1 − 4 + 9 = 1 + 2 + 3
1 − 4 + 9 − 16 = −(1 + 2 + 3 + 4).
Guess the general law suggested and prove it by induction.

 

[Deleted member 4993]

1 = 1,
1 − 4 = −(1 + 2)
1 − 4 + 9 = 1 + 2 + 3
1 − 4 + 9 − 16 = −(1 + 2 + 3 + 4).
Guess the general law suggested and prove it by induction.

Please show us what you have tried and exactly where you are stuck.

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[pka]

1 = 1,
1 − 4 = −(1 + 2)
1 − 4 + 9 = 1 + 2 + 3
1 − 4 + 9 − 16 = −(1 + 2 + 3 + 4).
Guess the general law suggested and prove it by induction.

As Mr Kahn pointed out, you must show some effort to do this problem.
Here is a hint: look at the LHS, \(\sum\limits_{k = 1}^n {{{\left( { - 1} \right)}^{k + 1}}{k^2}} \)

 

[Steven G]

1 = 1,
1 − 4 = −(1 + 2)
1 − 4 + 9 = 1 + 2 + 3
1 − 4 + 9 − 16 = −(1 + 2 + 3 + 4).
Guess the general law suggested and prove it by induction.

There is a difference between a free math help forum and a free math homework service site. One wants you to solve your own problem (with help) while the other will solve the problem for you.

 

[HallsofIvy]

There is a difference between a free math help forum and a free math homework service site. One wants you to solve your own problem (with help) while the other will solve the problem for you.

Except that there are no FREE math homework service sites!

 

[Steven G]

Except that there are no FREE math homework service sites!

You need to know where to look!