proof by induction question with summation
up vote
1
down vote
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$$sum_{i=1}^n(-1)^{i+1}i^2 = (-1)^{n+1}sum_{i=1}^n i.$$
im trying to prove thi by induction.
im starting from the LHS and trying to show the RHS after assuming true for n=k
$$sum_{i=1}^{k+1}(-1)^{i+1}i^2 = (-1)^{k+1}sum_{i=1}^k i + (-1)^{k+2}(k+1)^2$$
Is this right so far because im finding it hard to manipulate this to what i want. im ending up with a $k^2$ term which i dont know what to do with.
summation proof-writing induction
edited Nov 17 at 19:43
amWhy
191k27223437
asked Nov 17 at 19:37
hitherematey
577
add a comment |
up vote
1
down vote
favorite
$$sum_{i=1}^n(-1)^{i+1}i^2 = (-1)^{n+1}sum_{i=1}^n i.$$
im trying to prove thi by induction.
im starting from the LHS and trying to show the RHS after assuming true for n=k
$$sum_{i=1}^{k+1}(-1)^{i+1}i^2 = (-1)^{k+1}sum_{i=1}^k i + (-1)^{k+2}(k+1)^2$$
Is this right so far because im finding it hard to manipulate this to what i want. im ending up with a $k^2$ term which i dont know what to do with.
summation proof-writing induction
edited Nov 17 at 19:43
amWhy
191k27223437
asked Nov 17 at 19:37
hitherematey
577
Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
$$sum_{i=1}^n(-1)^{i+1}i^2 = (-1)^{n+1}sum_{i=1}^n i.$$
im trying to prove thi by induction.
im starting from the LHS and trying to show the RHS after assuming true for n=k
$$sum_{i=1}^{k+1}(-1)^{i+1}i^2 = (-1)^{k+1}sum_{i=1}^k i + (-1)^{k+2}(k+1)^2$$
Is this right so far because im finding it hard to manipulate this to what i want. im ending up with a $k^2$ term which i dont know what to do with.
summation proof-writing induction
edited Nov 17 at 19:43
amWhy
191k27223437
asked Nov 17 at 19:37
hitherematey
577
$$sum_{i=1}^n(-1)^{i+1}i^2 = (-1)^{n+1}sum_{i=1}^n i.$$
im trying to prove thi by induction.
im starting from the LHS and trying to show the RHS after assuming true for n=k
$$sum_{i=1}^{k+1}(-1)^{i+1}i^2 = (-1)^{k+1}sum_{i=1}^k i + (-1)^{k+2}(k+1)^2$$
Is this right so far because im finding it hard to manipulate this to what i want. im ending up with a $k^2$ term which i dont know what to do with.
summation proof-writing induction
summation proof-writing induction
edited Nov 17 at 19:43
amWhy
191k27223437
asked Nov 17 at 19:37
hitherematey
577
edited Nov 17 at 19:43
amWhy
191k27223437
asked Nov 17 at 19:37
hitherematey
577
edited Nov 17 at 19:43
amWhy
191k27223437
edited Nov 17 at 19:43
amWhy
191k27223437
edited Nov 17 at 19:43
amWhy
191k27223437
191k27223437
asked Nov 17 at 19:37
hitherematey
577
asked Nov 17 at 19:37
hitherematey
577
asked Nov 17 at 19:37
hitherematey
577
577
Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42
add a comment |
Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42
Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Use formula for $sum_{i=1}^k i$
answered Nov 17 at 23:22
hitherematey
577
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Use formula for $sum_{i=1}^k i$
answered Nov 17 at 23:22
hitherematey
577
add a comment |
up vote
1
down vote
accepted
Use formula for $sum_{i=1}^k i$
answered Nov 17 at 23:22
hitherematey
577
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Use formula for $sum_{i=1}^k i$
answered Nov 17 at 23:22
hitherematey
577
Use formula for $sum_{i=1}^k i$
answered Nov 17 at 23:22
hitherematey
577
answered Nov 17 at 23:22
hitherematey
577
answered Nov 17 at 23:22
hitherematey
577
answered Nov 17 at 23:22
hitherematey
577
577
add a comment |
add a comment |
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Start with the base case. Have you written out the first few terms of your sums?
– amWhy
Nov 17 at 19:40
havent seen if this works, but i think the problem was not using formulas for summations, also why did people downvote?
– hitherematey
Nov 17 at 22:42