Observe the following patterns 1-121- 1-1 1-2-122- 2-1 1-2-3-123- 3-1 1-2-3-4-124- 4-1and find the value of each of the following 1-2-3-4-5-50

By observing given patternwe see that #160; 1 + 2 + — +n = 1/2 [n× (n=1)] now 1 + 2 + 3 + 4 + — +50 = 1/2 [50 ×] = 1275 #160; #160; #160; ...

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Sum of N Terms of an AP

Observe the f...

Question

Observe the following patterns
$1 = \frac{1}{2} (1 \times (1 + 1))$
$1 + 2 = \frac{1}{2} (2 \times (2 + 1))$
$1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))$
$1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))$
and find the value of each of the following
$1 + 2 + 3 + 4 + 5 + . . . . + 50$

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1 = \frac{1}{2} (1 \times (1 + 1))

1 + 2 = \frac{1}{2} (2 \times (2 + 1))

1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))

1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))

31 + 32 + . . . + 50

1 = \frac{1}{2} \{1 \times (1 + 1)\} 1 + 2 = \frac{1}{2} \{2 \times (2 + 1)\} 1 + 2 + 3 = \frac{1}{2} \{3 \times (3 + 1)\} 1 + 2 + 3 + 4 = \frac{1}{2} \{4 \times (4 + 1)\}

\frac{2 \times 3 \times 5}{6}

\frac{3 \times 4 \times 7}{6}

\frac{4 \times 5 \times 9}{6}

Find the value of.

(i) (3⁰ + 4⁻¹) × 2² (ii) (2⁻¹ × 4⁻¹) ÷2⁻²

(iii) (iv) (3⁻¹ + 4⁻¹ + 5⁻¹)⁰

(v)

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