Question
Download Solution PDFWhat is the value of
1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ................ 12 2- 112
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ................ 12 2- 112
Concept used:
We know some n number of consecutive term = n(n + 1)/2
Calculation:
1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 122 - 112
⇒ (1002 - 992) + (982 - 972) + (962 - 952) + (942 - 932) + ...... + (122 - 112)
⇒ (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + (96 - 95)(96 + 95) + (94 - 93)(94 + 93) + ...... + (12 - 11)(12 + 11)
⇒ 1(100 + 99) + 1(98 + 97) + 1(96 + 95) + 1(94 + 93) + ...... + 1(12 + 11)
⇒ 100 + 99 + 98 + 97 + 96 + 95 + 94 + 93 + ...... + 12 + 11
Now,
[100(100 + 1)]/2 - [10(10 + 1)]/2
⇒ 50 × 101 - 5 × 11
⇒ 5050 - 55
⇒ 4995
∴ The required answer is 4995.
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