Question

HELLO !!!! Brainly Use krne vale saare BHAIYON or BEHNO☺
Solve the given question ⬆️

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Answer 1

putting n=1 in both LHS and RHS
n³=1³=1=LHS
[n(n+1)/2]² =[1(1+1)/2]² =1 =RHS
LHS=RHS
hence P(n) is true
let P (k)be true
1³+2³+3³+.....+k³=[k(k+1)/2]² -1
to show p(k+1)be true
adding (k+1)³ both the side of eq 1
1³+2³+3³+...+k³+(k+1)³=[k(k+1)/2]² +(k+1)³
=(k+1)² [k²/4+(k+1)]
=(k+1)² [(k²+4k+4)/4]
={(k+1)²(k+2)²}/4
=[{(k+1) (k+2)}/2]²
hence P(k+1)is true
therefore P(n)is true for all n belong to N