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Question

The value of 30r=16(r+2)(r3) is equal to :

A
7782
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B
7787
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C
7790
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D
7780
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Solution

The correct option is A 7780
Let S=30r=16(r+2)(r3)=30r=1(r+2)(r3)15r=1(r+2)(r3)

=30r=1(r2r6)15r=1(r2r6)

[By using ni=1k2=12+22+32++n2=n(n+1)(2n+1)6]

=(r(r+1)(2r+1)6r(r+1)26r)r=30(r(r+1)(2r+1)6r(r+1)26r)r=15

=(30(30+1)(60+1)630(30+1)2180)(15(15+1)(30+1)615(15+1)290)

=7780

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