Question

3. If 1 +2+ 3+....+ p = 171, then find 1 + 2 + 3 +.....+ p.

Answer 1

QUESTION :
If 1 + 2 + 3 + ....... + p = 171 then find 1³ + 2³ + 3³ + ......... + p³

SOLUTION :
GIVEN :
sum of natural numbers up to p = 171

Sum of cubes of n natural numbers = [n(n+1)/2]²

1 + 2 + 3 + ....... + p = 171
Sum of natural numbers up to p = 171
p ( p + 1 )/2 = 171
1³ + 2³ + 3³ + ......... + p³ = (171)²
1³ + 2³ + 3³ + ......... + p³ = 171 x 171
1³ + 2³ + 3³ + ......... + p³ = 29241

Hence, 1³ + 2³ + 3³ + ......... + p³ = 29241.

HOPE THIS WILL HELP YOU...

Answer 2

solution :

given 1 + 2 + 3 + ....+ p = 171

Sum of first p natural numbers = 171

[p( p+1)/2] = 171

⇒ p(p+1) = 342

⇒ p(p+1) = 18( 18 +1 )

∴ p = 18

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