Question

Find 1.4.7 + 3.6.9 + 5.8.11 + 7.10.13 +.... upto n terms

Answer 1

Hey dear,

● Answer-

Sn = 2n^4 + 12n^3 + 17n^2 - 17n

● Explaination-

nth term in given series is given by-

tn = (2n-1)(2n+2)(2n+5)

tn = 8n^3 + 24n^2 + 6n - 10

To calculate sum of the series-

Sn = ∑ (8n^3 + 24n^2 + 6n - 10)

Sn = 8∑n^3 + 24∑n^2 + 6∑n - 10∑1

Sn = 8(n^2+n)^2/4 + 24n(n+1)(2n+1)/6 + 6n(n+1)/2 + 10n

Sn = 2n^4 + 12n^3 + 17n^2 - 17n

Therefore, sum upto n terms is 2n^4 + 12n^3 + 17n^2 - 17n .

Hope this help..