(1^3 +2^3 +3^3)^1/2
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Answered by
1
In the given series 1+2+3++....+n=k, S
n
=k represents the sum of natural numbers upto n. From this we have to find sum of cubes of natural numbers upto n. Thus, we can write the formula instead of the series and that is:
Sum of natural numbers is S
n
=
2
n(n+1)
, therefore, we have
S
n
=
2
n(n+1)
⇒k=
2
n(n+1)
......(1)
We know that the sum of cubes of n natural numbers is S
n
=[
2
n(n+1)
]
2
, thus consider the sum as follows:
1
3
+2
3
+3
3
+.......+n
3
=S
n
⇒1
3
+2
3
+3
3
+.......+n
3
=[
2
n(n+1)
]
2
⇒1
3
+2
3
+3
3
+.......+n
3
=k
2
(from(1))
Hence 1
3
+2
3
+3
3
+.......+n
3
=k
2
.
Answered by
0
Answer:
6
Step-by-step explanation:
the answer is 6 am I wright
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