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larsab
@larsab
August 2022
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Вычислить сумму 1*2+2*5+3*8+...+n*(3*n-1)
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oganesbagoyan
Verified answer
1(3*1 -1) +2(3*2 -1)+3(3*3 -1) + ..... +n(3*n -1) =
=3(1²+2² +3² +...... +n²) - (1+2+3+ .... +n) =3* n(n+1)(2n+1)/6 -n(n+1)/2=n²(n+1).
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Answers & Comments
Verified answer
1(3*1 -1) +2(3*2 -1)+3(3*3 -1) + ..... +n(3*n -1) ==3(1²+2² +3² +...... +n²) - (1+2+3+ .... +n) =3* n(n+1)(2n+1)/6 -n(n+1)/2=n²(n+1).