CA Foundation · Quantitative Aptitude · Sequence and Series
What is the value of the sum 1×2 + 2×3 + 3×4 + ... + 10×11?
The sum equals 440. The series of products of consecutive integers, k(k+1), adds up to n(n+1)(n+2)/3. Putting n = 10 gives 10×11×12 divided by 3, which is 440. Using 6 as the divisor or the plain sum of squares gives wrong values.
- A385
- B440Correct
- C220
- D550
Explanation
The sum of n terms of k(k+1) equals n(n+1)(n+2)/3. For n = 10 this is 10×11×12/3 = 440. The value 385 is only the sum of squares 1² to 10², and 220 results from wrongly dividing by 6.
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