question archive Perhaps you just mean to convert it from "summation form" ("sigma form") to a written out form? For something like ∑i=1ni2∑i=1ni2, the summation symbol ΣΣ just means to "add up"
Perhaps you just mean to convert it from "summation form" ("sigma form") to a written out form? For something like ∑i=1ni2∑i=1ni2, the summation symbol ΣΣ just means to "add up"
Subject:MathPrice: Bought3
Perhaps you just mean to convert it from "summation form" ("sigma form") to a written out form?
For something like ∑i=1ni2∑i=1ni2, the summation symbol ΣΣ just means to "add up". Putting an i=1i=1 underneath the summation symbol means to start the value of ii at 1. It is then assumed that ii keeps increasing by 1 until it reaches i=ni=n, where nn is the number above the summation symbol. The i2i2 represents the formula for the terms that get added, first when i=1i=1, then i=2i=2, then i=3i=3, etc..., until i=ni=n.
Therefore, the answer would be ∑i=1ni2=12+22+32+?+(n−1)2+n2∑i=1ni2=12+22+32+?+(n-1)2+n2.
This example is interesting in that there is a shortcut formula for adding up the first nn squares: it equals
n(n+1)(2n+1)6=13n3+12n2+16n.n(n+1)(2n+1)6=13n3+12n2+16n.
You should take the time to check that this works when, for instance, n=5n=5.
Perhaps you just mean to convert it from "summation form" ("sigma form") to a written out form?
For something like ∑i=1ni2∑i=1ni2, the summation symbol ΣΣ just means to "add up". Putting an i=1i=1 underneath the summation symbol means to start the value of ii at 1. It is then assumed that ii keeps increasing by 1 until it reaches i=ni=n, where nn is the number above the summation symbol. The i2i2 represents the formula for the terms that get added, first when i=1i=1, then i=2i=2, then i=3i=3, etc..., until i=ni=n.
Therefore, the answer would be ∑i=1ni2=12+22+32+?+(n−1)2+n2∑i=1ni2=12+22+32+?+(n-1)2+n2.
This example is interesting in that there is a shortcut formula for adding up the first nn squares: it equals
n(n+1)(2n+1)6=13n3+12n2+16n.n(n+1)(2n+1)6=13n3+12n2+16n.
You should take the time to check that this works when, for instance, n=5n=5.
