Question

if 1cube+2cube+3cube+..... k cube =8281 then find 1+2+3+....+k​

Answer 1

Answer:

91

Step-by-step explanation:

Given

1³ + 2³ + 3³ ..... + k³ = 8281  ( sum of cubes of first 'k' natural numbers)

To find:-    1 + 2 + 3 + 4 +....k ( sum of first 'k' natural numbers)

We know that

Sum of first 'n' natural numbers = n(n + 1)/2

Sum of the cubes of the first 'n' natural numbers = n²(n + 1)²/4

                                                                                 = [n(n + 1)/2]²

                                                 = ( Sum of first 'n' natural numbers )²

Given

Sum of the cubes of first 'k' natural numbers = 8281

⇒ k²(k + 1)²/4 = 8281

⇒[k(k + 1)/2]² = 8281

⇒k(k + 1)/2 = √8281

⇒k(k + 1)/2 = 91

∴Sum of first 'k' natural numbers = 1+2+3+...+k = 91

Answer 2

Answer:

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