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The value of 1 22 + 2 32 + + 100 (101)212 2 + 22 3 + + 1002 101 is
(1) 305301
General terms: r(r + 1)2 = r3 + 2r2 + r and r2(r + 1) = r3 + r2, r = 1 to 100
r = 5050, r2 = 100 101 2016 = 5050 67, r3 = 50502
Value = r3 + 2 r2 + r r3 + r2
= 5050(5050 + 134 + 1)5050(5050 + 67)
= 51855117 = 305301 (cancel 17)
Answer: (1)
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