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# Addition Tricks for Bank Exams Learn speed maths tricks to improve your calculation ability in bank exams. To get success in bank exams. we need to be smart in doing calculations faster and accurately. So we have to use some maths tricks while solving the aptitude section that traditional methods of solving.

Here we are providing some simple addition-tricks for bank exams with examples that are very much useful to crack the upcoming bank exams.

If you came across these types of additions we can follow this easy trick to solve in less time.

### Model 1:

1)     6 + 66 + 666+ 6666+ 66666+ 666666
= 6 × (123456)  ->  [Explanation: In above problem the number 6 repeated orderly 1 time, 2 times  …up to 6 times).] = 740736.

2)    4 + 44 + 444 + 4444 + 44444 + 444444
= 4 × (123456)
= 493824.

3) 7 + 77 + 777 + 7777 + 77777
= 7 × (1 2 3 4 5)
= 86415

### Model 2:

1)  6.6 + 66.66 + 666.666 + 6666.6666 + 66666.66666
= 6 × (12345)   +  [6 × (54321)]->  [Explanation: In above problem the number 6 repeated orderly 1 time, 2 times  …up to 6 times).] = 74070 + 3.25926 ( 5 numbers after decimal point)
= 74073.25926

2) 4.4 + 44.44 + 444.444 + 4444.4444
= [4× ( 1 2 3 4)] + [ 4×(4 3 2 1)]

= 4936  + 1.7284 ( 4 times repeatations after decimal point so keep decimal point upto 4 digits )

= 4937.7284.

### 1)  9.4 + 99.44 + 999.444 + 9999.4444

Step 1:
Before decimal point 9  repeated up to 4 times orderly from 1 time, 2 times …4 times. so multiply 9 with 1234.
[9 ×( 1234) ]  =  11106
Step 2:
After decimal point 4 repeated up to 4 times orderly from 1 to 4 numbers. So multiply 4 with (4321) and put the decimal point after 4 digits by counting from right to left.
[4 × (4321) ] = 1. 7284
Step 3:
11106  + 1.7284 = 11107.7284

### Model 4:

What is the sum of all even natural numbers below 100
Solution:
2 + 4+ 6 + 8 + 10 +……+98
Formula: Sum =n/2 (f + l)      [n = total numbers, f = first number, l= last number].
= 49/2 ( 2 + 98) = 49 × 50 = 2450

### Model 5:

#### Example 1:  1/2  + 1/6 + 1/12 + 1/20 + 1/30 +1/42 = ?

(a) 6/7

(b) 7/6

(c) 8/7

(d) 5/9 #### Example 2:  1/3 + 1/15 + 1/35 + 1/63 + 1/99 ### Model 6:

1. 2546 + 5480 + 3210
Here add all first digits in step 1, and then add all second digits and then 3rd digits and so on as shown below.
2546 + 5480 + 3210
10000 + 1100 + 130 + 6 =          11, 236.

2. 256 + 516 + 310.
1000 + 70 + 12 = 1082.

3. 5467 + 6752 + 8971 +8605. 4. 679 + 760 + 896
Add all first digits in step 1, and then add all second digits and then 3rd digits and so on as shown below.
2100 + 220 + 15.
2335.

5.6587 + 6540 + 5555 + 2345.
19000 + 1800 + 210 + 17
21, 027

## IBPS Shortcut Formulas useful to solve simplifications faster.

1. (a3 – b3) = (a-b) (a2 + ab + b2)
2. (a3 + b3) = (a+b) (a2 – ab + b2)
3. (a + b)2 + (a – b)2 = 2( a2 + b2)
4. a4 – b4 = (a –b) (a+b) (a2 – b2)
5. (a5-b5)=(a-b) [a4+a3b+a2b2+ab3+b4].

Sum of first n odd numbers

= 1 + 3 + 5 + ………… + (2n-1)= n2

Sum of first n even numbers

= 2 + 4 + 6 + …………+ 2n = n (n+1).

Sum of first n natural numbers

= 1+2+3 +4 + ……..+n = n(n+1)/2.

Sum of squares of first n natural numbers

=12 + 22 + 32 + 42 + 52 + 62 + …………+n2.

= [n (n+1)(2n+1)]/6.

Sum of cubes of first n natural numbers

= 13 + 23+33 + 43 + …… + n3

= [n(n+1)/2]2

1 + 2/3 + (2/3)2 + (2/3)3 + ……(2/3)n= 1/(1 -2/3)n

1/1.3 + 1/3.5 + 1/5.7 +.……. + 1/[(2n+1) (2n-1)] =?

Shortcut method:

1/gap [1/first – 1/(2n-1)]= n/(2n+1)         last number = 2n-1 =7

= 2n=8

=n=4.

= 4/(2*4 + 1) = 4/9

#### Geometric Progression: When the sum looks likes as below we have to find the total sum by using formula.

a + ar2 + ar3 + ar4 + …………… + arn

= Total sum = a (1-rn)/ 1-r.  [ a = first number]

Example: 2 + 2×32 + 2×33 + 2×34 + 2×35

= 2( 1- 35)/1-3

= 2( 1- 243)/(-2)

=242

#### Athematic Progression:

The sum of a, (a+d), (a+2d), (a+3d),……… (a+(n-1)d)

Total sum = n/2 [2a + (n-1) d]

= n/2 (first +last).

#### What is the sum of all even natural numbers below 100

2 + 4+ 6 + 8 + 10 +……+98

Formula:

Sum =n/2 (f + l)      [n = total numbers, f = first number, l= last number].

= 49/2 ( 2 + 98) = 49 × 50 = 2450 Here, we can split 12 as 4×3
Ans. is 4 . Here, we can split 12 as 4 × 3.
we take small number 3 as answer. Formula:

A(2 ^n  -1)/2^n)

3(2 ^4  -1)/2^4)

= 3(15/16) = 6 sqrt|  4 + 5/16 + 6/25 + 7/36   ( solve from right to left)

Explaination:   ( sqrt (49) = 7, then 7+ 29 =36, sqrt(36) =6, 6+19 =25, sqrt (25) =5…..)

sqrt(4 +5) = sqrt(9) = 3

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