Answer:
. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3 / ,
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
k(k + 1)(2k + 1)
, (1)
we will prove that the statement must be true for n = k + 1:
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
. (2)
The left-hand side of (2) can be written as
2 + (k + 1)2
.
In view of (1), this simplifies to:
By using first step
Put n=1
(1)². =(1+1)(2×1)/6
1. (2×3)/6=1
n=1 is true
Let be put n=k
Step-by-step explanation:
yan sagot ko if not correct pa correct nalng thank you
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Answers & Comments
Answer:
. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3 / ,
6
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
2 =
k(k + 1)(2k + 1)
6
, (1)
we will prove that the statement must be true for n = k + 1:
1
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
6
. (2)
The left-hand side of (2) can be written as
1
2 + 22 + 32 + · · · + k
2 + (k + 1)2
.
In view of (1), this simplifies to:
Answer:
By using first step
Put n=1
(1)². =(1+1)(2×1)/6
1. (2×3)/6=1
n=1 is true
Let be put n=k
Step-by-step explanation:
yan sagot ko if not correct pa correct nalng thank you