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Asked Nov 23, 2019
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#1

We
Section 3.1 Homework
1.
1+2+... +n' = 1n2 (n +1) for all natural numbers n.
1
+... +
n(n + 1)
1
1
+
1
n
2.
+
for all natural num
1(2) (2)3 3(4)
(n 1)
(n+1)
n+1
- for any r 1 and any ne N
1-r
3. Show that
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We Section 3.1 Homework 1. 1+2+... +n' = 1n2 (n +1) for all natural numbers n. 1 +... + n(n + 1) 1 1 + 1 n 2. + for all natural num 1(2) (2)3 3(4) (n 1) (n+1) n+1 - for any r 1 and any ne N 1-r 3. Show that

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Step 1

We prove this by mathematical in...

1+2+nn? (n+1) for all n E N
For n 1
Assume the result is true for N = k, that is
P+2t k+ 1)
Let n k1
Consider
+2(k+1)1+2 +... + k? + (k+1)
1
(k
4
-k+1
4
(k +1\ (k + 4k + 4)
4
Simplify above
(k+1}={(k+1}(& + 2j
+2
4
Hence, the result is true for = k +1
Thus, 123...+ n = -n (n+1 is true for all natural numbers N.
4
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1+2+nn? (n+1) for all n E N For n 1 Assume the result is true for N = k, that is P+2t k+ 1) Let n k1 Consider +2(k+1)1+2 +... + k? + (k+1) 1 (k 4 -k+1 4 (k +1\ (k + 4k + 4) 4 Simplify above (k+1}={(k+1}(& + 2j +2 4 Hence, the result is true for = k +1 Thus, 123...+ n = -n (n+1 is true for all natural numbers N. 4

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