If we combine two consecutive triangular numbers, we get?
2025
If we combine two consecutive triangular numbers, we get?
Answer: C. Perfect Square — Let the two consecutive triangular numbers be T_n = n(n+1)/2 and T_{n+1} = (n+1)(n+2)/2. Their sum is: T_n + T_{n+1} = n(n+1)/2 + (n+1)(n+2)/2 Factor out…
- A.
Rational Number
- B.
Whole Number
- C.
Perfect Square
- D.
Prime Number
Attempted by 194 students.
Show answer & explanation
Correct answer: C
Let the two consecutive triangular numbers be T_n = n(n+1)/2 and T_{n+1} = (n+1)(n+2)/2.
Their sum is:
T_n + T_{n+1} = n(n+1)/2 + (n+1)(n+2)/2
Factor out (n+1)/2:
(n+1)/2 * (n + n+2) = (n+1)/2 * (2n+2)
Simplify:
(n+1)/2 * 2(n+1) = (n+1)²
Thus, the sum is (n+1)², which is a perfect square.
हिन्दी उत्तर:
मान लीजिए दो क्रमागत त्रिभुज संख्याएँ T_n = n(n+1)/2 और T_{n+1} = (n+1)(n+2)/2 हैं।
उनका योग है:
T_n + T_{n+1} = n(n+1)/2 + (n+1)(n+2)/2
(n+1)/2 को बाहर निकालें:
(n+1)/2 * (n + n+2) = (n+1)/2 * (2n+2)
सरल करें:
(n+1)/2 * 2(n+1) = (n+1)²
इसलिए, योग (n+1)² है, जो एक पूर्ण वर्ग है।